Question

A fair die is tossed eight times. Find the probability that a prime number appears five times.

Answer 1

Answer:

number of sample space = 6^8

now five dice on which prime number appears, can be chosen from 8 dice in 8C5 ways

no. of prime numbers on dice is 3.

so prime numbers on 5 selected dice can appear in 3^5 ways.

now, the non selected dice should have non pre.number. the no. of ways is 3^3

total no. of ways = 8C5*3^5*3^3

56*3^8

probability = 56*3^8/6^8

= 56/2^8

= 56/256

= 7/32