Question

Three different coins are tossed together. Find the probability of getting (i) exactly two heads, (ii) at least two heads (iii) at least two tails.

Answer 1

Set of possible outcomes

= $\left\{\text{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}\right\}$.

(i) Let $E_1$ be the event of getting exactly two heads

$\therefore$ Favourable outcomes = $\left\{\text{HHT, HTH, THH}\right\}$

No. of favourable outcomes = 3

$P\left(E_1\right)=\frac{3}{8}$

(ii) Let $E_2$ be the event of getting atleast two heads.

$\therefore$ Favourable outcomes = $\left\{\text{HHT, HTH, THH, HHH}\right\}$

No. of favourable outcomes = 4

$P\left(E_2\right)=\frac{4}{8}=\frac{1}{2}$

(iii) Let $E_3$ be the even of getting atleast two tails.

$\therefore$ Favourable outcomes = $\left\{\text{HTT, THT, TTH, TTT}\right\}$

$P\left(E_3\right)=\frac{4}{8}=\frac{1}{2}$