Question

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.

Answer 1

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