Question

Solve the following problem :

If a fair coin is tossed 4 times, find the probability that it shows 3 heads

Answer 1

Let X denote the number of heads.

P(getting head) = p = ${\displaystyle \frac{1}{2}}$

∴ q = 1 – p = ${\displaystyle 1-\frac{1}{2}=\frac{1}{2}}$

Given, n = 4

∴ X ∼ B${\displaystyle (4,\frac{1}{2})}$
The p.m.f of X is given by

P(X = x) = ${\displaystyle {}^4{\text{C}}_x{\left(\frac{1}{2}\right)}^x{\left(\frac{1}{2}\right)}^{4-x},x}$ = 0, 1,....,4

P(getting 3 heads) = P(X = 3) = ${\displaystyle {}^4{\text{C}}_3{\left(\frac{1}{2}\right)}^3\left(\frac{1}{2}\right)}$

= ${\displaystyle \frac{4}{2^4}}$

= ${\displaystyle \frac{1}{4}}$.