Probability Word Problems Worksheet - Fill Online, Printable ... - Free Printable

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Let me solve each problem step by step and explain the reasoning behind each solution. If any of the problems are unclear or if there's additional context in the image that isn't reflected in the text, please let me know!

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Problem 1:

> A card is drawn from a standard deck of 52 cards. What is the probability of drawing a number that is square?

Solution:

- In a standard deck, the numbered cards are 2 through 10 (in each suit).
- The square numbers between 2 and 10 are: 4 and 9.
- Each number appears in 4 suits (hearts, diamonds, clubs, spades), so:
- Number of 4s = 4
- Number of 9s = 4
- Total favorable outcomes = 4 + 4 = 8
- Total possible outcomes = 52

$$
P(\text{square number}) = \frac{8}{52} = \frac{2}{13}
$$

✔ Answer: $ \frac{2}{13} $

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Problem 2:

> Each of the letters in the word SAMSUNG are on separate cards, face down on the table. If you pick a card at random, what is the probability that the letter will be S or U?

Solution:

- Letters in "SAMSUNG": S, A, M, S, U, N, G → total of 7 letters
- Count of S = 2
- Count of U = 1
- So, favorable outcomes for S or U = 2 + 1 = 3
- Total possible outcomes = 7

$$
P(S \text{ or } U) = \frac{3}{7}
$$

✔ Answer: $ \frac{3}{7} $

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Problem 3:

> A magician showed a magic trick where he picked one card from a standard deck. Determine the probability that the card will be a queen card?

Solution:

- There are 4 queens in a standard deck (one per suit)
- Total cards = 52

$$
P(\text{queen}) = \frac{4}{52} = \frac{1}{13}
$$

✔ Answer: $ \frac{1}{13} $

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Problem 4:

> A bag contains ten black marbles, twenty white marbles, and five grey marbles. You pick one marble at random. What is the probability that the marble will be either white OR black?

Solution:

- Black marbles = 10
- White marbles = 20
- Grey marbles = 5
- Total marbles = 10 + 20 + 5 = 35
- Favorable outcomes (white or black) = 10 + 20 = 30

$$
P(\text{white or black}) = \frac{30}{35} = \frac{6}{7}
$$

✔ Answer: $ \frac{6}{7} $

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Problem 5:

> You ask a friend to think of a number from four to twelve. What is the probability that his number will be 8?

Solution:

- Numbers from 4 to 12 inclusive: 4, 5, 6, 7, 8, 9, 10, 11, 12 → total = 9 numbers
- Only one number is 8

$$
P(8) = \frac{1}{9}
$$

✔ Answer: $ \frac{1}{9} $

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Problem 6:

> Each of letters in the word CAMEL are on separate cards, face down on the table. If you pick a card at random, what is the probability that the letter will be L or E?

Solution:

- Letters in "CAMEL": C, A, M, E, L → 5 distinct letters
- E appears once, L appears once
- So favorable outcomes = 2

$$
P(L \text{ or } E) = \frac{2}{5}
$$

✔ Answer: $ \frac{2}{5} $

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Problem 7:

> You roll a SIX sided die. What is the probability that the value of the roll will be one?

Solution:

- A six-sided die has faces: 1, 2, 3, 4, 5, 6
- Only one outcome is "1"

$$
P(1) = \frac{1}{6}
$$

✔ Answer: $ \frac{1}{6} $

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Problem 8:

> A bag contains 5 blue sticks, 4 red sticks, and 9 orange sticks and you ask a friend to pick one without looking. What is the probability that the stick will be blue?

Solution:

- Blue = 5
- Red = 4
- Orange = 9
- Total sticks = 5 + 4 + 9 = 18

$$
P(\text{blue}) = \frac{5}{18}
$$

✔ Answer: $ \frac{5}{18} $

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Problem 9:

> You think of a number from the first twenty negative integers. What is the probability that the integer chosen will be divisible by 4?

Solution:

- First 20 negative integers: -1, -2, -3, ..., -20
- We want numbers divisible by 4: i.e., multiples of 4
- Multiples of 4 between -1 and -20: -4, -8, -12, -16, -20 → that’s 5 numbers

$$
P(\text{divisible by 4}) = \frac{5}{20} = \frac{1}{4}
$$

✔ Answer: $ \frac{1}{4} $

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Problem 10:

> When a six-sided die is rolled then what is the probability that the number rolled will be even?

Solution:

- Even numbers on a die: 2, 4, 6 → 3 outcomes
- Total outcomes = 6

$$
P(\text{even}) = \frac{3}{6} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{2}{13} $ |
| 2 | $ \frac{3}{7} $ |
| 3 | $ \frac{1}{13} $ |
| 4 | $ \frac{6}{7} $ |
| 5 | $ \frac{1}{9} $ |
| 6 | $ \frac{2}{5} $ |
| 7 | $ \frac{1}{6} $ |
| 8 | $ \frac{5}{18} $ |
| 9 | $ \frac{1}{4} $ |
| 10 | $ \frac{1}{2} $ |

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