Question

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.

Answer 1

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)`