Question

What is the probability that in group of 10 random people, at least two of them have the same letter in initials (such as LMS for Laurel Marie Sander), assuming that each triple of initials is equally likely.

Answer 1

Answer:

So the probability is P=0.00256.

Step-by-step explanation:

We have 26 letters, so the probability that the first letter in the name is the same is 1/26.

The probability that the second letter in the name is the same is 1/26 and the probability that the third letter in the name is the same is 1/26.

Out of ten people we choose 2.

So the probability is:

$P=C_2^{10}\left(\frac{1}{26}\right)^3\\\\P=\frac{10!}{2!(10-2)!}\cdot \left(\frac{1}{26}\right)^3\\\\P=\frac{45}{17576}\\\\P=0.00256$

So the probability is P=0.00256.