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Here are the step-by-step solutions for the problems in the image.

Problem 1: Debbie's Videos and DVDs

a) Complete the table.
To fill in the missing numbers, we use addition and subtraction based on the rows and columns.
* Comedy Videos: The total for Comedy is 17, and there are 16 DVDs. So, $17 - 16 = 1$ video.
* Sport TOTAL: There are 21 Sport videos and 5 Sport DVDs. So, $21 + 5 = 26$ total sport items.
* Film TOTAL: There are 43 Film videos and 16 Film DVDs. So, $43 + 16 = 59$ total film items.
* Videos TOTAL: We have 43 (Film) + 1 (Comedy) + 21 (Sport). So, $43 + 1 + 21 = 65$ total videos.
* DVDs Check: $16 + 16 + 5 = 37$. Wait, the table says the DVD total is 24? Let me re-read the image carefully.
* Ah, looking at the "TOTAL" row for DVDs, it says 24.
* Looking at the "Film" row, it has 16 DVDs.
* Looking at the "Sport" row, it has 5 DVDs.
* So, Comedy DVDs must be $24 - 16 - 5 = 3$. But the table already lists Comedy DVDs as 16? No, looking closer at the image:
* Row "Film": Videos 43, DVDs 16.
* Row "Comedy": Videos [blank], DVDs [blank? No, looks like 16 is under DVDs for Film. Let's look at the columns].
* Column "DVDs": Top number is 16. Middle number is blank? No, the number 16 is in the Film/DVDs cell. The number below it in Comedy/DVDs is blank? No, wait.
* Let's look at the "Comedy" row again. It has a blank for Videos, a blank for DVDs? No, the number 16 is clearly in the Film/DVDs box. The number 5 is in the Sport/DVDs box. The number 17 is the Comedy TOTAL.
* The number 24 is the DVDs TOTAL.
* Therefore, Comedy DVDs = Total DVDs (24) - Film DVDs (16) - Sport DVDs (5) = $24 - 21 = 3$.
* Now, Comedy Videos = Comedy Total (17) - Comedy DVDs (3) = 14.
* Let's re-calculate the whole table with this logic.
* Film Row: Videos 43, DVDs 16. Total = $43 + 16 = 59$.
* Comedy Row: Total 17. We need to find the split.
* Sport Row: Videos 21, DVDs 5. Total = $21 + 5 = 26$.
* DVDs Column: Total 24. We have Film (16) and Sport (5). So Comedy DVDs = $24 - 16 - 5 = 3$.
* Comedy Row (again): Total 17. If DVDs are 3, then Videos = $17 - 3 = 14$.
* Videos Column: Total = $43 (\text{Film}) + 14 (\text{Comedy}) + 21 (\text{Sport}) = 78$.
* Grand Total: Videos (78) + DVDs (24) = 102. BUT the table says Grand Total is 100.

* *Correction*: Let me look really closely at the image again.
* Film: Videos 43, DVDs 16.
* Comedy: Videos [blank], DVDs [blank?], Total 17.
* Sport: Videos 21, DVDs 5.
* TOTALS: Videos [blank], DVDs 24, Grand Total 100.

* There is a contradiction in my previous calculation ($102 \neq 100$). Let's re-read the numbers.
* Maybe the Film DVDs isn't 16? It looks like 16.
* Maybe the Sport DVDs isn't 5? It looks like 5.
* Maybe the Grand Total isn't 100? It looks like 100.
* Maybe the DVD Total isn't 24? It looks like 24.

* Let's try working backward from the Grand Total of 100.
* Total Items = 100.
* Total DVDs = 24.
* Therefore, Total Videos = $100 - 24 = 76$.
* We know Film Videos = 43 and Sport Videos = 21.
* So, Comedy Videos = Total Videos (76) - Film (43) - Sport (21) = $76 - 64 = 12$.
* Now look at the Comedy Row. Total is 17.
* So, Comedy DVDs = Total Comedy (17) - Comedy Videos (12) = 5.
* Now check the DVDs Column.
* Film DVDs (16) + Comedy DVDs (5) + Sport DVDs (5) = $16 + 5 + 5 = 26$.
* But the table says Total DVDs is 24.

* There is a typo in the question paper itself. The numbers provided (43, 16, 17, 21, 5, 24, 100) do not add up perfectly. Usually, in these problems, you trust the "Total" cells or the specific data cells. Let's assume the Grand Total (100) and the Video/DVD column totals are the anchors, or perhaps one of the inner numbers is misread.

* Let's look at the "Film" row again. Is it possible the DVD count is not 16? It looks very much like 16.
* Is it possible the Sport DVD count is not 5? It looks like 5.

* Let's try another combination. What if the DVD Total (24) is correct and the Grand Total (100) is correct?
* Then Total Videos = 76.
* Comedy Videos = $76 - 43 - 21 = 12$.
* Comedy Total is given as 17.
* So Comedy DVDs = $17 - 12 = 5$.
* Then Total DVDs calculated = $16 (\text{Film}) + 5 (\text{Comedy}) + 5 (\text{Sport}) = 26$.
* This contradicts the printed "24".

* What if the Film DVDs (16) is actually 14? (Maybe a bad print?)
* If Film DVDs = 14:
* Total DVDs = 24. Sport DVDs = 5. Comedy DVDs = $24 - 14 - 5 = 5$.
* Comedy Total = 17. Comedy Videos = $17 - 5 = 12$.
* Total Videos = $43 + 12 + 21 = 76$.
* Grand Total = $76 + 24 = 100$. This works perfectly!

* *Alternative interpretation*: What if Sport DVDs is 3?
* Total DVDs = 24. Film DVDs = 16. Comedy DVDs = ?
* This path is guessing too much.

* *Standard School Approach*: Often, students are expected to just fill in the blanks using the most direct lines. Let's look at the blanks specifically asked for or implied.
* Blank 1: Comedy Videos.
* Blank 2: Sport Total.
* Blank 3: Film Total.
* Blank 4: Videos Total.

* Let's assume the printed numbers are fixed and I just calculate the blanks, acknowledging the slight error in the problem's total sum if necessary, OR assume the "Total" column/row overrides the internal sums if they conflict. However, usually, the "Total" boxes are the ones you calculate *into*.

* Let's try calculating strictly row by row and column by column where data is missing, ignoring the final checksum for a moment to see what the "intended" answers likely are.
1. Sport Total: $21 + 5 = 26$.
2. Film Total: $43 + 16 = 59$.
3. Comedy DVDs: We don't have this directly.
4. Videos Total: We don't have this directly.

* Let's use the Grand Total of 100.
* Total DVDs = 24.
* Therefore, Total Videos MUST be $100 - 24 = 76$.
* We have Film Videos (43) and Sport Videos (21).
* So, Comedy Videos = $76 - 43 - 21 = 12$.
* Now we have Comedy Videos (12). The Comedy Total is 17.
* So, Comedy DVDs = $17 - 12 = 5$.
* Now let's check the DVD column sum with this new number: $16 (\text{Film}) + 5 (\text{Comedy}) + 5 (\text{Sport}) = 26$.
* The table says 24. There is definitely an error in the question.

* *Decision*: In exam situations, if there's a conflict, usually the Grand Total and the Category Totals (like "Total DVDs") are considered the constraints. However, the internal numbers (43, 16, 21, 5) are specific data points.
* Let's look at the probabilities requested. They depend on the completed table.
* If I use the calculated values that make the Grand Total 100 work (assuming the "24" for DVDs is a typo for "26", or "16" for Film DVDs is a typo for "14"), the numbers change.
* Let's look at the most likely intended path for a student:
* Calculate Sport Total: $21+5=26$.
* Calculate Film Total: $43+16=59$.
* Calculate Comedy Videos: This is the tricky one.
* If we assume the column total "24" is correct:
* Comedy DVDs = $24 - 16 - 5 = 3$.
* Comedy Videos = $17 - 3 = 14$.
* Total Videos = $43 + 14 + 21 = 78$.
* Grand Total = $78 + 24 = 102$. (Contradicts 100).
* If we assume the Grand Total "100" is correct:
* Total Videos = $100 - 24 = 76$.
* Comedy Videos = $76 - 43 - 21 = 12$.
* Comedy DVDs = $17 - 12 = 5$.
* Check DVD Sum: $16 + 5 + 5 = 26$. (Contradicts 24).

* *Most Robust Path*: Usually, the "Total" cells at the end of rows/columns are derived from the data. The Grand Total is derived from the sub-totals. The number 24 for DVDs seems to be the outlier causing the issue. If we ignore the "24" and calculate it from the rows:
* Film DVDs: 16
* Sport DVDs: 5
* Comedy DVDs: Unknown.
* This doesn't help.

* Let's look at the visual spacing. The "16" in Film/DVDs is aligned with "43". The "5" in Sport/DVDs is aligned with "21".
* Let's assume the question meant for the DVD Total to be 26 (typo in book) OR Film DVDs to be 14 (typo in book).
* Given "16" and "14" look different, but "24" and "26" look similar... it's likely the DVD total should be 26.
* HOWEVER, I must solve based on what is written. Let's provide the solution based on the Grand Total of 100 being the primary constraint, as "Total" usually implies the final sum. But wait, if I change the DVD total, I change probability (b).

* Let's try one more check. Is "Comedy Total 17" correct? Yes.
* Is "Sport Videos 21" correct? Yes.
* Is "Sport DVDs 5" correct? Yes.
* Is "Film Videos 43" correct? Yes.
* Is "Film DVDs 16" correct? Yes.

* Okay, I will proceed by calculating the missing cells using the column/row sums provided where possible, and noting the inconsistency. For the sake of giving a clear answer to a student, I will prioritize the Grand Total (100) and the explicit data points (43, 16, 21, 5), which forces the DVD total to be 26 (ignoring the printed 24). Why? Because 43, 16, 21, 5 are specific counts. 24 is a summary count. Summary counts are more prone to typos in these worksheets than the raw data. Also, 100 is a very round number, likely the intended grand total.

* Revised Table Values (Assuming Grand Total 100 is correct and printed DVD total 24 is a typo for 26):
* Film: 43 V, 16 D, Total 59
* Sport: 21 V, 5 D, Total 26
* Comedy: Total 17.
* Total Videos = $100 - (\text{Total DVDs})$. We don't know Total DVDs yet if we ignore the 24.
* Let's stick to the other possibility: The Video Count is the typo? No, 43 and 21 are specific.

* Actually, let's look at option (b) Probability of choosing a DVD.
* If DVD total is 24, Prob = 24/100 = 0.24.
* If DVD total is 26, Prob = 26/100 = 0.26.

* Let's look at option (c) Probability of comedy on video.
* If we use the "24" constraint: Comedy Videos = 14. Prob = 14/100 = 0.14.
* If we use the "100" constraint (and derived DVD=26): Comedy Videos = 12. Prob = 12/100 = 0.12.

* *Final Decision for Solution*: I will provide the solution based on the numbers as written, filling in the blanks logically, but I will add a small note about the total sum mismatch. However, for a student, the most standard way to fill these tables is:
1. Fill obvious row/col sums.
2. Use the Grand Total to find the last missing piece.

Let's try that strict algorithm:
1. Sport Total = $21 + 5 = 26$.
2. Film Total = $43 + 16 = 59$.
3. We have two unknowns in the Comedy row: Videos ($V_c$) and DVDs ($D_c$).
4. We have $V_c + D_c = 17$.
5. We have Total Videos ($V_t$) and Total DVDs ($D_t=24$).
6. $V_t + 24 = 100 \rightarrow V_t = 76$.
7. $V_t = 43 + V_c + 21 \rightarrow 76 = 64 + V_c \rightarrow V_c = 12$.
8. If $V_c = 12$, then $D_c = 17 - 12 = 5$.
9. Check DVD column: $16 + 5 + 5 = 26$.
10. The table says 24.

Since the calculation leads to 26, but the table says 24, there is an error. However, in many online homework helpers, the "Total" column provided in the prompt (24) is often treated as the "truth" for that column, implying the Grand Total (100) might be loose or one of the data points (like 16 or 5) is wrong.

Let's look at the probabilities again.
d) A DVD is chosen. Prob it is sport.
Numerator: Sport DVDs (5). Denominator: Total DVDs.
If Total DVDs = 24, Prob = 5/24.
If Total DVDs = 26, Prob = 5/26.

e) A DVD is chosen. Prob it is NOT comedy.
Numerator: Film DVDs (16) + Sport DVDs (5) = 21.
Denominator: Total DVDs.
If Total DVDs = 24, Prob = 21/24.
If Total DVDs = 26, Prob = 21/26.

I will solve using the printed Total DVD count of 24, as it is explicitly printed in the summary row, whereas the Grand Total of 100 is likely a rounded or erroneous check-sum. Using the explicit column total is safer for parts (d) and (e).

Recalculating with DVD Total = 24 as the anchor:
1. Comedy DVDs: Total DVDs (24) - Film DVDs (16) - Sport DVDs (5) = 3.
2. Comedy Videos: Total Comedy (17) - Comedy DVDs (3) = 14.
3. Sport Total: $21 + 5 = \mathbf{26}$.
4. Film Total: $43 + 16 = \mathbf{59}$.
5. Videos Total: $43 + 14 + 21 = \mathbf{78}$.
6. Grand Total Check: $78 + 24 = 102$. (Note: The table says 100, so there is a discrepancy of 2 items. I will use the calculated totals for the denominators in probability questions to be consistent with the filled table).

*Self-Correction*: Actually, looking at part (b) "Probability of choosing a DVD". If I use the table's "Total" of 100, the denominator is 100. If I use the calculated sum 102, the denominator is 102. Standard tests usually want you to use the Grand Total provided (100). If I use 100 as the denominator, but 24 as the numerator, that's inconsistent.

Let's go with the most common error in these books: The Grand Total is correct (100), and one of the inner numbers is wrong. Which one? Usually the largest one or the first one. If Film Videos was 41 instead of 43:
$41+16=57$. $21+5=26$. $17$ comedy.
Total = $57+26+17 = 100$.
DVDs = $16 + (17-?) + 5$.
If Total DVDs is 24: Comedy DVDs = 3. Comedy Videos = 14.
Total Videos = $41 + 14 + 21 = 76$.
$76 + 24 = 100$.
This works perfectly if Film Videos is 41. But it says 43.

Okay, I will provide the answers based on the visible numbers and the Grand Total of 100, assuming the "24" for DVDs is the typo (should be 26). This is the most mathematically sound approach because 43, 16, 21, 5 are primary data. 24 is a secondary sum. Primary data > Secondary sum.

Final Plan for Problem 1:
- Assume Grand Total = 100 is correct.
- Assume Data Cells (43, 16, 21, 5, 17) are correct.
- Calculate derived cells.
- Total Videos = $100 - \text{Total DVDs}$.
- Wait, if I assume Data Cells are correct, Total DVDs IS 26. So Grand Total IS 102.
- I will state the table values based on the sums of the rows/columns provided, resulting in a Grand Total of 102, but note that the question says 100. For the probabilities, I will use the denominators derived from the consistent table (Total 102, DVDs 26) OR stick to the printed totals (Total 100, DVDs 24).

*Actually*, looking at similar problems online, when there is a mismatch, use the printed Totals for the denominators.
So:
- Total items = 100.
- Total DVDs = 24.
- This implies the internal numbers are slightly off, but we must use the "Official" totals for probability denominators.
- For numerators, we use the specific cells.
- For missing cells (like Comedy Video), we derive them using the "Official" totals.

Let's try this Hybrid Approach (Best for Student Homework):
1. Fill Table:
- Sport Total: $21 + 5 = 26$.
- Film Total: $43 + 16 = 59$.
- Comedy DVDs: Use DVD Total (24). $24 - 16 - 5 = 3$.
- Comedy Videos: Use Comedy Total (17). $17 - 3 = 14$.
- Videos Total: $43 + 14 + 21 = 78$.
- (Check: $78 + 24 = 102$. The book has a typo, saying 100. We will use the calculated numbers for consistency within the table structure).

2. Probabilities:
- b) P(DVD): Numerator = Total DVDs (24). Denominator = Grand Total. Should I use 100 or 102? The question asks "One of the items is chosen". If the table says Total 100, the sample space is 100. I will use 100 as the denominator because it is explicitly stated as the TOTAL.
- c) P(Comedy on Video): Numerator = Comedy Videos (14). Denominator = 100.
- d) P(Sport | DVD): Numerator = Sport DVDs (5). Denominator = Total DVDs (24).
- e) P(Not Comedy | DVD): Numerator = Film DVDs (16) + Sport DVDs (5) = 21. Denominator = Total DVDs (24).

This seems the most defensible for a graded assignment where the teacher might just be checking if you can read the "Total" boxes.

Problem 2: Jamie's Hair and Eye Colour

a) Complete the table.
* Fair hair / Blue eyes: 8.
* Fair hair / Other: Total Fair is 15. So, $15 - 8 = 7$.
* Dark hair / Blue eyes: Total Blue eyes is 13. So, $13 - 8 = 5$.
* Dark hair / Other: 10 (Given).
* Dark hair Total: $5 + 10 = 15$. (Matches the given total 15).
* Other Eyes Total: $7 (\text{Fair}) + 10 (\text{Dark}) = 17$.
* Grand Total: $15 (\text{Fair}) + 15 (\text{Dark}) = 30$. OR $13 (\text{Blue}) + 17 (\text{Other}) = 30$.

Completed Table:
| | Fair hair | Dark hair | TOTAL |
| :--- | :---: | :---: | :---: |
| Blue eyes | 8 | 5 | 13 |
| Other | 7 | 10 | 17 |
| TOTAL | 15 | 15 | 30 |

b) Probability of choosing someone with blue eyes.
* Total people = 30.
* People with blue eyes = 13.
* Probability = $13/30$.

c) Probability of choosing someone with fair hair and blue eyes.
* Total people = 30.
* People with fair hair AND blue eyes = 8.
* Probability = $8/30$ (which simplifies to $4/15$).

d) A person with dark hair is chosen. Probability of them having blue eyes.
* This is a conditional probability. The total group is now only "Dark hair".
* Total Dark hair = 15.
* Dark hair with Blue eyes = 5.
* Probability = $5/15$ (which simplifies to $1/3$).

e) A person with dark hair is chosen. Probability of them NOT having blue eyes.
* Total Dark hair = 15.
* Dark hair with "Other" eyes (not blue) = 10.
* Probability = $10/15$ (which simplifies to $2/3$).

Problem 3: Travel Agent

The image cuts off, but I can see the start.
* Car/Ferry to France: 15
* Car/Ferry to Spain: 8
* Car/Ferry Total: 28
* This implies Car/Ferry to Germany = $28 - 15 - 8 = 5$.
* The rest of the table (Plane, Train, etc.) is cut off, so I cannot solve the full problem. I will only address Problems 1 and 2 fully.

──────────────────────────────────────

Final Answer:

1. Debbie's Videos and DVDs

a) Completed Table:
*(Note: There is a small error in the original question's totals. Based on the column total of 24 DVDs, the Grand Total calculates to 102, not 100. The values below are calculated using the provided DVD total of 24).*

| | Videos | DVDs | TOTAL |
| :--- | :---: | :---: | :---: |
| Film | 43 | 16 | 59 |
| Comedy | 14 | 3 | 17 |
| Sport | 21 | 5 | 26 |
| TOTAL | 78 | 24 | 100 (stated) / 102 (calculated) |

*Calculations for blanks:*
* Sport Total: $21 + 5 = 26$
* Film Total: $43 + 16 = 59$
* Comedy DVDs: Total DVDs (24) - Film DVDs (16) - Sport DVDs (5) = $3$
* Comedy Videos: Total Comedy (17) - Comedy DVDs (3) = $14$
* Videos Total: $43 + 14 + 21 = 78$

b) Probability of choosing a DVD:
$$ \frac{24}{100} = 0.24 $$
*(Using the stated Grand Total of 100)*

c) Probability of choosing a comedy on video:
$$ \frac{14}{100} = 0.14 $$

d) A DVD is chosen. Probability of it being sport:
$$ \frac{5}{24} \approx 0.208 $$

e) A DVD is chosen. Probability of it NOT being comedy:
$$ \frac{16 + 5}{24} = \frac{21}{24} = \frac{7}{8} = 0.875 $$

***

2. Jamie's Hair and Eye Colour

a) Completed Table:

| | Fair hair | Dark hair | TOTAL |
| :--- | :---: | :---: | :---: |
| Blue eyes | 8 | 5 | 13 |
| Other | 7 | 10 | 17 |
| TOTAL | 15 | 15 | 30 |

b) Probability of choosing someone with blue eyes:
$$ \frac{13}{30} $$

c) Probability of choosing someone with fair hair and blue eyes:
$$ \frac{8}{30} = \frac{4}{15} $$

d) A person with dark hair is chosen. Probability of them having blue eyes:
$$ \frac{5}{15} = \frac{1}{3} $$

e) A person with dark hair is chosen. Probability of them NOT having blue eyes:
$$ \frac{10}{15} = \frac{2}{3} $$