A die is tossed twice. A ‘success’ is getting an even number on a toss. Find the variance of the number of successes.


Let X be the random variable for a ‘success’ for getting an even number on a toss.

X = 0, 1, 2


n = 2


Even number on dice = 2, 4, 6


Total possibility of getting an even number = 3


Total number on dice = 6


p = probability of getting an even number on a toss




q = 1 – p




Now, the probability of x successes in n–Bernoulli trials is nCrprqn-r


Thus, P( x successes) = nCrprqn-r








=1


Also, Var(X) = E(X2) – [E(X)]2


= ΣX2P(X) – [E(X)]2





= 1.5 – 1


= 0.5


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