Question

Roll a die 4 times. (a) What is the probability of getting 4 times the same face? (b) What is the probability of getting 3 times the same face?

Answer 1

Solution:

number of times a die is rolled = n = 4

probability of rolling one of the faces = p = 1 / 6 = 0.1666

let x be one of the faces on a die ,

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

probability distribution table of number of times x is rolled

x	P( x)
0	0.4824
1	0.3857
2	0.1157
3	0.0154
4	0.0008

( a )

Probability of rolling x , 4 times = 0.0008

there are 6 faces on a die. so.,

probability of getting 4 times the same face = 6 * 0.0008 = 0.0048

( b )

Probability of rolling x , 3 times = 0.0154

there are 6 faces on a die. so.,

probability of getting times the same face = 6 * 0.0154 = 0.0924