# In a game, the entry fee is of ₹ 5.

Question:

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.

Solution:

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

$=\{(H T T),(T H T),(T T H),(H H T),(H T H),(T H H)\}$

$\therefore \quad n\left(E_{3}\right)=6$

$\therefore \quad P\left(E_{3}\right)=\frac{n\left(E_{3}\right)}{n(S)}=\frac{6}{8}=\frac{3}{4}$