Question

How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?

A. 1
B. 2
C. 3
D. 4
E. 5

Answer 1

Answer:

Given and Find:

★ How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?

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We know that:

★ Probability of getting leap year for a single person = $\sf{\dfrac{1}{4}}$

★ The term "n" refers the number of possible chances.

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Calculations:

→ $\sf{1 - \bigg(\dfrac{3}{4}\bigg)^{n}}$

→ $\sf{\bigg(\dfrac{3}{4}\bigg)^{n} \: lesser \: than \: \bigg(\dfrac{1}{2}\bigg)}$

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• 1/2 = 50℅
• 1/4 = 25℅

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Therefore, the probability of getting the 50℅ needs least 2 people.