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
(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 E1 = Event that Sweta losses the entry fee
= She tosses tail on three times
n(E1) = {(T T T)}
(ii) Let Event that Sweta gets double entry fee
= She tosses tail on three times = {(HHH)}
n(E2) = 1
(iii) Let Event that Sweta gets her entry fee back
= Sweta gets heads one or two times
= {(HTT),(THT),(TTH),(HHT),(HTH),(THH)}
n(E3) = 6
