Crispy ABC

Probability Level 3

You've just bought a bag of 26 26 alphabet biscuits from A to Z. When you pick 5 5 biscuits out randomly, what is the probability in percentage that at least one of them is a vowel alphabet (A, E, I, O, U)?

Give your answer to the nearest integer.


The answer is 69.

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Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

The probability of getting at least 1 vowel alphabet = (100%) - (probability of getting no vowel alphabets)

The probability of getting no vowel alphabets happens when we pick 5 out of other non-vowel 21 alphabets. The number of ways to pick 5 out of 21 is 21C5.

The probability of getting no vowel alphabets = 21 C 5 26 C 5 \frac{21C5}{26C5} = 17 × 18 × 19 × 20 × 21 22 × 23 × 24 × 25 × 26 \frac{17 \times 18 \times 19 \times 20 \times 21}{22 \times 23 \times 24 \times 25 \times 26} ≈ 31%.

Therefore, the probability of getting at least 1 vowel alphabet = 100% - 31% = 69%.

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