PROBABILITIES - Word problems worksheet - Free Printable

Let’s solve each problem one by one.

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Problem 1:
Jolly draws a card from 30 cards numbered 1 to 30. What’s the probability of drawing a square number?

Step 1: List square numbers between 1 and 30.
Squares: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25 → 6² = 36 (too big)
So: 1, 4, 9, 16, 25 → that’s 5 numbers.

Step 2: Total possible outcomes = 30

Step 3: Probability = favorable / total = 5/30 = 1/6 (simplified)

Decimal: 1 ÷ 6 ≈ 0.1667
Percentage: 0.1667 × 100 ≈ 16.67%

✔ Checked: 5 squares out of 30 → correct.

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Problem 2:
Word: APPLE → letters: A, P, P, L, E → total 5 cards.

We want probability of picking A or L.

A appears once, L appears once → total favorable = 2

Total cards = 5

Probability = 2/5

Decimal: 2 ÷ 5 = 0.4
Percentage: 0.4 × 100 = 40%

✔ Checked: A and L are both present once → 2 out of 5 → correct.

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Problem 3:
Standard deck = 52 cards.

Black queens: Queen of Spades and Queen of Clubs → 2 cards.

Probability = 2/52 = 1/26 (simplified)

Decimal: 1 ÷ 26 ≈ 0.0385
Percentage: 0.0385 × 100 ≈ 3.85%

✔ Checked: Only two black queens in a deck → correct.

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Problem 4:
Bag has:
- Red marbles: 5
- Black marbles: 15
- White marbles: 10

Total marbles = 5 + 15 + 10 = 30

We want red OR white → 5 + 10 = 15

Probability = 15/30 = 1/2

Decimal: 0.5
Percentage: 50%

✔ Checked: Half the marbles are red or white → correct.

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Problem 5:
Friend thinks of a number from 2 to 11 inclusive.

How many numbers? 2,3,4,5,6,7,8,9,10,11 → that’s 10 numbers.

Only one of them is 5.

Probability = 1/10

Decimal: 0.1
Percentage: 10%

✔ Checked: 10 choices, only one is 5 → correct.

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Problem 6:
Word: OPPORTUNITIES

Let’s count the letters:

O, P, P, O, R, T, U, N, I, T, I, E, S → let’s list them:

Positions:
1. O
2. P
3. P
4. O
5. R
6. T
7. U
8. N
9. I
10. T
11. I
12. E
13. S

Total letters: 13

Now, how many O’s? Positions 1 and 4 → 2 O’s
How many I’s? Positions 9 and 11 → 2 I’s

So favorable = 2 (O) + 2 (I) = 4

Probability = 4/13

Decimal: 4 ÷ 13 ≈ 0.3077
Percentage: ≈ 30.77%

✔ Checked: Counted all letters and O/I occurrences → correct.

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Final Answer:

1. Fraction: 1/6, Decimal: 0.1667, Percentage: 16.67%
2. Fraction: 2/5, Decimal: 0.4, Percentage: 40%
3. Fraction: 1/26, Decimal: 0.0385, Percentage: 3.85%
4. Fraction: 1/2, Decimal: 0.5, Percentage: 50%
5. Fraction: 1/10, Decimal: 0.1, Percentage: 10%
6. Fraction: 4/13, Decimal: 0.3077, Percentage: 30.77%