Question

Three coins are tossed simultaneously. Find the probability of getting exactly two heads.

Answer 1

Finding the probability of getting exactly two heads.

Let $\text{P}\left(\text{E}\right)$ be the probability of getting exactly two heads.

All possible outcomes when three coins are tossed simultaneously$=\text{HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}$

$\therefore$Number of possible outcomes$=8$

Outcomes having exactly two heads$=HHT,HTH,THH$

$\therefore$Number of favourable outcomes$=3$

We know that $\text{P}\left(\text{E}\right)\text{=}\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$

So, $\text{P}\left(\text{E}\right)$$=\frac{3}{8}$

Hence, probability of getting exactly two heads$=\frac{\mathbf{3}}{\mathbf{8}}$