Question

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

Answer 1

Let E be the event of getting even number on tossing a die.

∴ P(E) = `3/6 = 1/2` and `"P"(bar"E") = 1 - 1/2 = 1/2`

Here X = 0, 1, 2

P(X = 0) = `"P"(bar"E")*"P"(bar"E")`

= `1/2*1/2`

= `1/4`

P(X = 1) = `"P"("E")*"P"(bar"E") + "P"(bar"E")*"P"("E")`

= `1/2*1/2 + 1/2*1/2`

= `1/4 + 1/4`

= `2/4`

P(X = 2) = P(E).P(E) 

= `1/2*1/2`

= `1/4`

∴ Probability distribution table is

X	0	1	2
P(X)	`1/4`	`2/4`	`1/4`

E(X) = `0 xx 1/4 + 1 xx 2/4 + 2 xx 1/4`

= `2/4 + 2/4`

= 1

E(X²) = `0 xx 1/4 + 1 xx 2/4 + 4 xx 1/4`

= 3/2`

∴ Variance (X) = E(X²) – [E(X)]²

= `3/2 - 1`

= `1/2`

= 0.5