Question

Find the probability of a least one birthday match among a group of 38 people.

The probability is approximately ..... ​(Round to four decimal places as​ needed.)

Answer 1

The probability that no one shares the same birthday out of a group of 38 people.

The first student can be born on any day, so we’ll give him a probability of 365/365.

The next student is now limited to 364 possible days, so the second student’s probability is 364/365.

The third student may be born on any of the remaining 363 days, so 363/365.

This pattern continues so that our last student has a probability of 328/365

Hence Probability,

= 0.135932

Probability of a least one birthday match among a group of 38 people is,

= 1 - 0.135932 = 0.8641 (ans)

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