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10-144.

FINDING BIRTHDAY TWINS

If you randomly select a group of just $21$ people the chance of there being a pair of people with the same birthday is greater than $50\%$. This surprising fact is due to the large number of pairings possible in a group of $21$ people.

1. Determine the number of possible unique pairings in a group of $21$ people.

Unique pairings refer to the number of combinations of $2$.

2. Compute the probability that any given pair of people have the same birthday (ignoring leap day).

$\left(\frac{1}{365}\right)=0.002740$

3. Compute the probability that any given pair of people do not have the same birthday (ignoring leap day).

See part (b).

4. Now compute the probability that exactly one pair out of the $21$ people has the same birthday.

Use the answers from parts (a) – (c) to determine the probability.