# Solve the following problem : Find the probability of the number of successes in two tosses of a die, where success is defined as six appears in at least one toss. - Mathematics and Statistics

Sum

Solve the following problem :

Find the probability of the number of successes in two tosses of a die, where success is defined as six appears in at least one toss.

#### Solution

Success is defined as a number six appears on at least one die.
Let X denote the number of successes.
∴ possible values of X are 0, 1, 2.

Let P(getting six) = p =(1)/(6)

∴ q = 1 – p = 1 - (1)/(6) = (5)/(6)

∴ P(X = 0) = P(no success) = qq = q2 =  (25)/(36)

P(X =1) = P(one success) pq + qp = 2pq

= 2 xx (1)/(6) xx (5)/(6)

= (10)/(36)

P(X = 2) = P(two successes) = pp = p2 = (1)/(36)

∴ Probability distribution of X is as follows:

 X 0 1 2 P(X = x) (25)/(36) (10)/(36) (1)/(36)
Concept: Random Variables and Its Probability Distributions
Is there an error in this question or solution?