1.pdf - Name: Date Topic : Probability Word Problems- Worksheet 1 ... - Free Printable

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

1. Coin and Die
* Step 1: Find the probability of flipping heads on a coin. There are 2 sides (Heads, Tails), so the chance is $\frac{1}{2}$.
* Step 2: Find the probability of rolling a 3 on a standard die. There are 6 numbers (1-6), so the chance is $\frac{1}{6}$.
* Step 3: Since these are independent events happening together ("and"), multiply the probabilities:
$$ \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} $$

2. Drawing Cards (SAMSUNG)
* Step 1: Count the total letters in SAMSUNG. There are 7 letters total.
* Step 2: Count the letter 'S'. There are 2 'S's. The probability of drawing an 'S' first is $\frac{2}{7}$.
* Step 3: After drawing one card, there are 6 cards left. If the first was an 'S', there is only 1 'S' left. The probability of drawing an 'S' second is $\frac{1}{6}$.
* Step 4: Multiply the probabilities:
$$ \frac{2}{7} \times \frac{1}{6} = \frac{2}{42} $$
* Step 5: Simplify the fraction by dividing top and bottom by 2:
$$ \frac{1}{21} $$

3. Magic Trick (Queen of Clubs)
* Step 1: A standard deck has 52 cards.
* Step 2: There is only 1 Queen of Clubs in the deck.
* Step 3: The probability is simply 1 out of 52.
$$ \frac{1}{52} $$

4. Drawing Red then Black
* Step 1: Total cards = 52. Red cards (Hearts + Diamonds) = 26.
* Step 2: Probability of first card being Red: $\frac{26}{52}$ (which simplifies to $\frac{1}{2}$).
* Step 3: One card is gone, so 51 remain. There are still 26 Black cards.
* Step 4: Probability of second card being Black: $\frac{26}{51}$.
* Step 5: Multiply them:
$$ \frac{1}{2} \times \frac{26}{51} = \frac{26}{102} $$
* Step 6: Simplify by dividing by 2:
$$ \frac{13}{51} $$

5. Rolling Two Dice (Sum of 7)
* Step 1: Total possible outcomes when rolling two dice is $6 \times 6 = 36$.
* Step 2: List the pairs that add up to 7:
* (1, 6)
* (2, 5)
* (3, 4)
* (4, 3)
* (5, 2)
* (6, 1)
* That is 6 successful outcomes.
* Step 3: The probability is $\frac{6}{36}$.
* Step 4: Simplify:
$$ \frac{1}{6} $$

6. Lottery (Choosing 3 numbers from 10)
* Step 1: This is a combination problem because the order doesn't matter. We need to choose 3 numbers from 10.
* Step 2: Calculate the number of ways to pick 3 numbers from 10 ($_{10}C_3$):
$$ \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = \frac{720}{6} = 120 $$
* Step 3: There is only 1 winning combination.
* Step 4: The probability is:
$$ \frac{1}{120} $$

7. Spinner (Not Blue)
* Step 1: The spinner has 8 equal sections.
* Step 2: 3 are Blue. That means $8 - 3 = 5$ sections are NOT Blue.
* Step 3: The probability is 5 out of 8.
$$ \frac{5}{8} $$

8. Drawing Marbles (Blue then Green)
* Step 1: Total marbles = $5 (\text{Red}) + 3 (\text{Blue}) + 4 (\text{Green}) = 12$.
* Step 2: Probability of first being Blue: $\frac{3}{12}$ (simplifies to $\frac{1}{4}$).
* Step 3: One marble is gone, so 11 remain. There are still 4 Green marbles.
* Step 4: Probability of second being Green: $\frac{4}{11}$.
* Step 5: Multiply them:
$$ \frac{1}{4} \times \frac{4}{11} = \frac{4}{44} $$
* Step 6: Simplify:
$$ \frac{1}{11} $$

9. Survey (Female AND Dislikes Computer Games)
* Step 1: Look at the table. Find the row for "Female" and the column for "Dislikes". The number where they meet is 10.
* Step 2: Find the total number of students surveyed. Add all the numbers in the table: $15 + 20 + 10 + 5 = 50$.
* Step 3: The probability is 10 out of 50.
* Step 4: Simplify:
$$ \frac{10}{50} = \frac{1}{5} $$

10. Raffle Ticket (Winning)
* Step 1: You bought 5 tickets.
* Step 2: Total tickets sold = 200.
* Step 3: The probability is your tickets over total tickets.
$$ \frac{5}{200} $$
* Step 4: Simplify by dividing by 5:
$$ \frac{1}{40} $$

Final Answer:
1. 1/12
2. 1/21
3. 1/52
4. 13/51
5. 1/6
6. 1/120
7. 5/8
8. 1/11
9. 1/5
10. 1/40