Question

In an experiment of tossing a fair coin three times, find the P(X=2), P(X > 1) and P(1 ≤ X < 2). Let X be the random variable giving the number of tails.

Answer 1

Sample space: {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

$P(X=2)=\frac{3}{8}=0.375.$

$P(X>1)=P(X=2)+P(X=3)=\frac{3}{8}+\frac{1}{8}=\frac{1}{2}=0.5.$

$P(1\le X<2)=P(X=1)=\frac{3}{8}=0.375.$