## Suppose that we ask n randomly selected people whether they share your birthday. a. Give an expression for the probability that no one share

Question

Suppose that we ask n randomly selected people whether they share your birthday. a. Give an expression for the probability that no one shares your birthday (ignore leap years). b. How many people do we need to select so that the probability is at least .5 that at least one shares your birthday?

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2022-01-07T14:07:06+00:00
2022-01-07T14:07:06+00:00 1 Answer
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## Answers ( )

Answer:

n = 253 people

Step-by-step explanation:

There are ‘n’ persons and at least one person should share your birthday, the probability is given by

1 – (364/365)^n

We want this probability to be at least 0.5

Therefore, 1 – (364/365)^n ≥ 0.5

It mathematically becomes:

(364/365)^n ≥ 0.5

Taking In of both sides

In(364/365)^n ≤ In(0.5)

n.In(364/365) ≤ In (0.5)

Therefore,

n ≥ In 0.5/In 364/365

n ≥ 252.652

n = 253

Which implies we need at least 253 people.