Question

Solve the following problem :

Find the probability of the number of successes in two tosses of a die, where success is defined as number greater than 4.

Answer 1

Success is defined as a number greater than 4 appears on at least one die.
Let X denote the number of successes.
∴ Possible values of X and 0, 1, 2.
Let, P(getting a number greater than 4) = p = `(2)/(6) = (1)/(3)`

∴ q = 1 – p = `1 - (1)/(3) = (2)/(3)`

∴ P(X = 0) = P(no success) = qq = q² = `(4)/(9)`

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

= `(2 xx 1)/(3) xx (2)/(3)`

= `(4)/(9)`

P(X = 2) = P(two successes) = pp = p² = `(1)/(9)`

∴ Probability distribution of X is as follows:

X	0	1	2
P(X = x)	`(4)/(9)`	`(4)/(9)`	`(1)/(9)`