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Question

A coin is tossed three times, where E is the event of atmost two tails, F is the event of atleast one tail. Then the value of P(E/F) is:

A
67
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B
68
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C
37
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D
38
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Solution

The correct option is A 67
The sample space of the given experiment will be:
S={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
Here, E: atmost two tails
And F: atleast one tail
E={HHH,HHT,HTH,THH,HTT,THT,TTH} and F={HHT,HTH,THH,HTT,THT,TTH,TTT}
So, P(E)=78,P(F)=78,P(EF)=68=34
Now we know that
By definition of conditional probability
P(E/F)=P(EF)P(F)
P(E/F)=3/47/8=67

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