A group of people is introducing themselves to each other at the beginning of a

ID: 3069501 • Letter: A

Question

A group of people is introducing themselves to each other at the beginning of a conference.

Assume throughout the problem that everyone has a name spelled using the 26 letters of the

English alphabet, and that each letter is equally likely to appear.

Two people are the first to sit down at their table. What is the probability

that their first names do

not

start with the same letter?

They are joined by a third person. What is the probability that the three

persons’ first names all start with different letters?

What is the probability that some pair of the three people have first names

starting with the same letter?

a) Number of letters available for second persons name after excluding the first letter of the first person's name = 26- 1 = 25

P(two people will not have names starting with same letter) = 1 x 25/26

= 25/26

= 0.9615

b) P(all three have different letters at the starting of their first name) = 1 x 25/26 x 24/26

= 150/169

= 0.8876

c) P(a pair having first letter of name the same) = 1 - P(none having same first letter) - P(all having same first letter)

= 1 - 0.8876 - 1x1/26 x 1/26

= 0.1109

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