Question 38(i)
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 loses the entry fee.

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Solution

Total possible outcomes of tossing a coin 3 times,
S = {(HHH), (TTT), (HTT), (THT), (TTH), (THH), (HTH), (HHT)}
$∴ n (S) = 8$
Let $E_{1}$ = Event that Sweta losses the entry fee
= She tosses tail on three times
$n (E_{1}) = {(T T T)}$
$P (E_{1}) = \frac{n (E_{1})}{n (S)} = \frac{1}{8}$

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Total possible outcomes of tossing a coin 3 times, S = {(HHH), (TTT), (HTT), (THT), (TTH), (THH), (HTH), (HHT)} ∴n(S)=8 Let E1 = Event that Sweta losses the entry fee = She tosses tail on three times n(E1)={(TTT)} P(E1)=n(E1)n(S)=18

Total possible outcomes of tossing a coin 3 times,
S = {(HHH), (TTT), (HTT), (THT), (TTH), (THH), (HTH), (HHT)}
$∴ n (S) = 8$
Let $E_{1}$ = Event that Sweta losses the entry fee
= She tosses tail on three times
$n (E_{1}) = {(T T T)}$
$P (E_{1}) = \frac{n (E_{1})}{n (S)} = \frac{1}{8}$