Question

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

Answer 1

Success is defined as a number six appears on at least one die.

Let X denotes the number of successes.

∴ The 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`