In a game, the entry fee is of ₹ 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
(i) loses the entry fee.
(ii) gets double entry fee.
(iii) just gets her entry fee.
Total possible outcomes of tossing a coin 3 times,
S = {(HHH), (TTT), (HTT), (THT), (TTH), (THH), (HTH), (HHT)}
∴ n (S) = 8
(i) Let $E_{1}=$ Event that Sweta losses the entry fee
$=$ She tosses tail on three times
$n\left(E_{1}\right)=\{(T T T)\}$
$P\left(E_{1}\right)=\frac{n\left(E_{1}\right)}{n(S)}=\frac{1}{8}$
(ii) Let $E_{2}=$ Event that Sweta gets double entry fee
$=$ She tosses heads on three times $=\{(H H H)\}$
$n\left(E_{2}\right)=1$
$\therefore \quad P\left(E_{2}\right)=\frac{n\left(E_{2}\right)}{n(S)}=\frac{1}{8}$
(iii) Let $E_{3}=$ Event that Sweta gets her entry fee back
$=$ Sweta gets heads one or two times
$=\{(H T T),(T H T),(T T H),(H H T),(H T H),(T H H)\}$
$\therefore \quad n\left(E_{3}\right)=6$
$\therefore \quad P\left(E_{3}\right)=\frac{n\left(E_{3}\right)}{n(S)}=\frac{6}{8}=\frac{3}{4}$