Question

A fair coin is tossed 6 times. Find the probability of getting heads 4 times.

Answer 1

Here n = 6

Let p = Getting head in a single toss (success)

∴ p = `1/2`

∴ q = `1 - p = 1/2`

Let x = Number of heads out of 6

Then `X ∼ B(n = 6,  p = 1/2)`

The p.m.f. of X is given by

P(X = x) = P(x)

= `""^6C_x(1/2)^x(1/2)^(6-x)`

x = 0, 1, 2, 3, 4, 5, 6

∴ P(X = 4) = P(4)

= `""^6C_4(1/4)^4(1/2)^2`

= `(6 xx 5)/2*1/16*1/4`

= `15/64`

= 0.234