Let's solve each problem step by step from the worksheet titled
"Independent Practice 2: Elementary Probability". We'll go through each question, explain the reasoning, and compute the probability.
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1. Find the probability of picking up a 10 from a deck of cards.
- A standard deck has
52 cards.
- There are
4 tens (one in each suit: hearts, diamonds, clubs, spades).
- So, probability = favorable outcomes / total outcomes
$$
P(10) = \frac{4}{52} = \frac{1}{13}
$$
✔ Answer: $ \frac{1}{13} $
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2. Find the probability of selecting an even number from the list: 11, 12, 13, 14, 15, 16, 17.
- List: 11, 12, 13, 14, 15, 16, 17 → Total = 7 numbers
- Even numbers: 12, 14, 16 → 3 evens
- $$
P(\text{even}) = \frac{3}{7}
$$
✔ Answer: $ \frac{3}{7} $
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3. Find the probability of flipping a tail on a coin.
- A fair coin has two sides: Heads (H), Tails (T)
- $$
P(\text{tail}) = \frac{1}{2}
$$
✔ Answer: $ \frac{1}{2} $
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4. Find the probability of picking a green or yellow marble from a box that contains one of each color: green, yellow, blue, red.
- Marbles: green, yellow, blue, red → 4 marbles
- Green or yellow = 2 favorable outcomes
- $$
P(\text{green or yellow}) = \frac{2}{4} = \frac{1}{2}
$$
✔ Answer: $ \frac{1}{2} $
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5. Find the probability of selecting a penny from a purse containing:
- 2 pennies
- 1 nickel
- 1 dime
- 1 quarter
- Total coins = 2 + 1 + 1 + 1 = 5
- Favorable (pennies) = 2
- $$
P(\text{penny}) = \frac{2}{5}
$$
✔ Answer: $ \frac{2}{5} $
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6. Find the probability of picking a black card from a deck of cards.
- A standard deck has 52 cards:
- 26 red (hearts, diamonds)
- 26 black (spades, clubs)
- $$
P(\text{black}) = \frac{26}{52} = \frac{1}{2}
$$
✔ Answer: $ \frac{1}{2} $
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7. Find the probability of spinning a square on the wheel.
- The image shows a spinner divided into 8 equal sections.
- Count the squares: there are
2 squares (black squares).
- Total sections = 8
- $$
P(\text{square}) = \frac{2}{8} = \frac{1}{4}
$$
✔ Answer: $ \frac{1}{4} $
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8. Find the probability of rolling a 3 on a six-sided die.
- Die has faces: 1, 2, 3, 4, 5, 6 → 6 outcomes
- Only one face is a 3
- $$
P(3) = \frac{1}{6}
$$
✔ Answer: $ \frac{1}{6} $
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9. Find the probability of rolling an odd number on a die.
- Odd numbers on a die: 1, 3, 5 → 3 odds
- Total outcomes = 6
- $$
P(\text{odd}) = \frac{3}{6} = \frac{1}{2}
$$
✔ Answer: $ \frac{1}{2} $
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10. Find the probability of picking a yellow marble from a bag containing two yellow marbles and four green marbles.
- Yellow = 2
- Green = 4
- Total = 2 + 4 = 6
- $$
P(\text{yellow}) = \frac{2}{6} = \frac{1}{3}
$$
✔ Answer: $ \frac{1}{3} $
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11. Find the probability of spinning a Z on the wheel.
- The wheel has 4 sections: X, X, Z, X
- So, 3 X's and 1 Z
- $$
P(Z) = \frac{1}{4}
$$
✔ Answer: $ \frac{1}{4} $
---
12. Find the probability of spinning an X on the wheel.
- From above: 3 X's out of 4 sections
- $$
P(X) = \frac{3}{4}
$$
✔ Answer: $ \frac{3}{4} $
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13. Find the probability of selecting a penny from a purse containing:
- 4 pennies
- 2 nickels
- 1 dime
- 1 quarter
- Total coins = 4 + 2 + 1 + 1 = 8
- Pennies = 4
- $$
P(\text{penny}) = \frac{4}{8} = \frac{1}{2}
$$
✔ Answer: $ \frac{1}{2} $
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✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | $ \frac{1}{13} $ |
| 2 | $ \frac{3}{7} $ |
| 3 | $ \frac{1}{2} $ |
| 4 | $ \frac{1}{2} $ |
| 5 | $ \frac{2}{5} $ |
| 6 | $ \frac{1}{2} $ |
| 7 | $ \frac{1}{4} $ |
| 8 | $ \frac{1}{6} $ |
| 9 | $ \frac{1}{2} $ |
| 10 | $ \frac{1}{3} $ |
| 11 | $ \frac{1}{4} $ |
| 12 | $ \frac{3}{4} $ |
| 13 | $ \frac{1}{2} $ |
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of probability worksheet high school.
