Question

In a game the entry fee is ₹5. The game consists of tossing coins 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 head, she receivers double 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 entey fee (iii) just gets her entry fee. Select the correct answer from above options

Answer 1

One coin is tossed 3 times so total number of favourable outcomes `= 2^(3) = 8`, which are (HHH),(HHT), (THH) and (replacing ` H to T and T to H`) (TTT),(TTH),(THT),(HTT). (i) Losing the game means getting no head. Number of favourable outcomes of getting no head = F(E) = 1 So, `= P(E) = (F(E))/(T(E)) = (1)/(8)` So, probability (losing the entry fee) i.e., `P(E) = (F(E))/(T(E)) = (1)/(8)` ltbr. (ii) Gets double entry fee back by getting 3 heads. Number of favourable outcomes of getting 3 heads i.e, F(E) = 1 `therefore` Probability (getting double entry fee ) P(E) `= (F(E))/(T(E)) = (1)/(8)` (iii) Just gets her enrty fees back by getting either one or two head, Number of favouarble outcomes of getting either one or two heads, i.e, F(E) =6 `therefore` Probability (just getting entry fee) i.e.,`P(E) = (F(E))/(T(E)) = (6)/(8) =(3)/(4)`