Question

How many people are needed so that the probability that at least one of them has the same first and last name initials as you is at least 3/4?

Answer 1

The probability that at least one of them has the same first and last name initials is to be computed here.

Probability that a person has the same first and last name initial is computed here as:
= (1/26)2

= 1/676

Therefore, probability that at least one of the k people has the same first and last name initials is computed here as:
= 1 - Probability that none of the k people have the same first and last name initials

= 1 - (1 - (1/676))k

Now we want this to be at least 0.75, therefore we get here:

1 - (1 - (1/676))k >= 0.75

(1 - (1/676))k <= 0.25

(675/676)k <= 0.25

k >= Ln(0.25) / Ln(675/676)

k >= 936.44

Therefore 937 is the minimum sample size required here.