Question

Question 38(iii)
In a game, the entry fee is of Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she
just gets her entry fee.

Answer 1

Total possible outcomes of tossing a coin 3 times,
S = {(HHH), (TTT), (HTT), (THT), (TTH), (THH), (HTH), (HHT)}
$\therefore n\left(S\right)=8$
Let $E_3$ = Event that Sweta gets her entry fee back
= Sweta gets heads one or two times
= {(HTT), (THT), (TTH), (HHT), (HTH), (THH)}
$\therefore n\left(E_3\right)=6$
$\therefore P\left(E_3\right)=\frac{n\left(E_3\right)}{n\left(S\right)}=\frac{6}{8}=\frac{3}{4}$