Question

5 fair 8-sided dice are rolled.

(a)	Find the conditional probability that at least one die lands on 3 given that all 5 dice land on different numbers.

Answer 1

Bayes' Theorem: P(A | B) = P(A & B)/P(B)

Number of ways in which 5 different numbers can be landed = 8C5

= 56

Number of ways in which 5 different numbers can b elanded such that 1 number is 3 = 1 x Number of ways in which 4 numbers can be landed from 7

= 1 x 7C4

= 35

P(at least one die lands on 3 given that all 5 dice land on different numbers) = Number of ways in which 5 different numbers can b elanded such that 1 number is 3 / Number of ways in which 5 different numbers can be landed Number of ways in which 5 different numbers can be landed

= 35/56

= 0.625