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Q.

In a game, the entry fee is Rs 5. The game consists of 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, what is the probability that she loses the entry fee?

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a

\frac{1}{8}

b

\frac{5}{8}

c

1

d

\frac{3}{8}

answer is A.

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Detailed Solution

Given that in a game, the game consists of tossing a coin 3 times.
Let us assume that P(B) is the probability of an event “B”, n(S) is the total number of events in the sample space and n(B) is the number of favorable outcomes.
The total number of possible outcomes are

H H H

,

T T T

,

H T T

,

T H T

,

T T H

,

T H H

,

H T H

,

H H T

.
So,

n S = 8

.
Let B be the event that Sweta losses the entry fee that is she tosses tail on all the three times,

T T T

.
So,

n B = 1

.
The probability is,

P B = Number of favourable outcomes Total number of outcomes P B = n B n S P B = 18

Therefore, 1 is the correct option.

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