Probability Word Problems Worksheet with Answers PDF | airSlate ... - Free Printable

Here are the solutions to the probability problems on your worksheet. I have worked through each one step-by-step to ensure the answers are correct.

1. Cards numbered 1 to 20
* Total outcomes: There are 20 cards in total.
* Favorable outcomes (Square numbers): We need to find numbers between 1 and 20 that are perfect squares ($1\times1$, $2\times2$, etc.).
* $1^2 = 1$
* $2^2 = 4$
* $3^2 = 9$
* $4^2 = 16$
* $5^2 = 25$ (This is too big, so we stop here).
* The square numbers are: 1, 4, 9, 16. There are 4 of them.
* Probability: $\frac{4}{20}$. This simplifies to $\frac{1}{5}$.

2. SMSUNG card trick
* Total outcomes: The word "SMSUNG" has 6 letters.
* Favorable outcomes (Letter 'S'): Let's count the S's. S-M-S-U-N-G. There are 2 S's.
* Probability: $\frac{2}{6}$. This simplifies to $\frac{1}{3}$.

3. Magic show (8 or Queen)
* Total outcomes: A standard deck has 52 cards.
* Favorable outcomes:
* There are four 8s (one for each suit).
* There are four Queens (one for each suit).
* Total favorable cards = $4 + 4 = 8$.
* Probability: $\frac{8}{52}$. Both numbers can be divided by 4. This simplifies to $\frac{2}{13}$.

4. Marbles in a bag
* Total outcomes: Add all the marbles together: $3 \text{ (black)} + 5 \text{ (white)} + 2 \text{ (grey)} = 10$ marbles.
* Favorable outcomes (Not black): We want white or grey. $5 + 2 = 7$ marbles.
* Probability: $\frac{7}{10}$.

5. Number from four to twelve
* Total outcomes: List the numbers: 4, 5, 6, 7, 8, 9, 10, 11, 12. Counting them gives us 9 total numbers.
* Favorable outcomes (Odd numbers): From that list, the odd numbers are 5, 7, 9, 11. There are 4 odd numbers.
* Probability: $\frac{4}{9}$.

6. Word PROBABILITY
* Total outcomes: Count the letters in P-R-O-B-A-B-I-L-I-T-Y. There are 11 letters.
* Favorable outcomes (Letter B or L):
* There are two B's.
* There is one L.
* Total = $2 + 1 = 3$.
* Probability: $\frac{3}{11}$.

7. Six-sided die (Value of 6)
* Total outcomes: A die has 6 sides (1, 2, 3, 4, 5, 6).
* Favorable outcomes: There is only one side with a 6 on it.
* Probability: $\frac{1}{6}$.

8. Bag of sticks
* Total outcomes: Add the sticks: $5 \text{ (blue)} + 4 \text{ (red)} + 3 \text{ (orange)} = 12$ sticks.
* Favorable outcomes (Blue): There are 5 blue sticks.
* Probability: $\frac{5}{12}$.

9. Integers 1 to 20 (Divisible by 4)
* Total outcomes: Numbers 1 through 20. Total is 20.
* Favorable outcomes: Multiples of 4 up to 20 are: 4, 8, 12, 16, 20. There are 5 numbers.
* Probability: $\frac{5}{20}$. This simplifies to $\frac{1}{4}$.

10. Two dice rolled (Sum is even)
* Total outcomes: Each die has 6 sides. $6 \times 6 = 36$ total possible combinations.
* Favorable outcomes: An even sum happens if both dice are Even (Even + Even = Even) OR both dice are Odd (Odd + Odd = Even).
* Even numbers on a die: 2, 4, 6 (3 numbers).
* Odd numbers on a die: 1, 3, 5 (3 numbers).
* Combinations where both are Even: $3 \times 3 = 9$.
* Combinations where both are Odd: $3 \times 3 = 9$.
* Total favorable outcomes: $9 + 9 = 18$.
* Probability: $\frac{18}{36}$. This simplifies to $\frac{1}{2}$.

Final Answer:
1. 1/5
2. 1/3
3. 2/13
4. 7/10
5. 4/9
6. 3/11
7. 1/6
8. 5/12
9. 1/4
10. 1/2