Question

An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is

• A. 1/9
• B. 1/8
• C. 2/3
• D. 3/8

Answer 1

The correct option is D 3/8

n = 3 (No. of tosses)
then p = P (success) $=P\left(H\right)=\frac{1}{2}$

and q = P (failure = P(T) $=\frac{1}{2},$

Let X = (No. of Heads) and success = Head.
then P (X = r success) $={}^n{C}_r{p}^r{q}^{n-r}$

So, probability of exactly two heads

$=P(X=2)={}^3{C}_2{\left(\frac{1}{2}\right)}^2\left(\frac{1}{2}\right)$

$P=\frac{3}{8}$