PROBLEM 17E

Each of the 12 students in a class is given a fair 12-sided die. In addition, each student is numbered from 1 to 12.

(a) If the students roll their dice, what is the probability that there is at least one “match” (e.g., student 4 rolls a 4)?

(b) If you are a member of this class, what is the probability that at least one of the other 11 students rolls the same number as you do?

Answer :

Step 1 of 2:

Each of 12 students in a class is given a fair 12-sided die. In addition,each student is numbered from 1 to 12.

a).

If the students roll their dice,we have to find the probability that there is at least one “match” .

Here A={at least one match} and

=none of them “match”

So P(A) = 1 - P()

P(at least one ‘match’) = 1-P(none of them “match”)

P(at least one ‘match’) = 1-

P(at least one ‘match’) = 1-