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Question

A fair coin is tossed five times. If the out comes are 2 heads and 3 tails (in some order), then what is the probability that the fourth toss is a head?

A
14
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B
25
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C
12
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D
35
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Solution

The correct option is A 25
A fair coin is tossed 5 times
E=2 heads are obtained on first two tosses.
F=3 tails are obtained on next three tosses.
Sample space,
S=[HHHHH,HHHHT,HHHTH,HHTHH,HTHHH,THHHH,TTHHH,HTTHH,
HHTTH,HHHTT,THHHT,HTHTH,THTHH,HHTHT,TTTHH,HTTTH,HHTTT,
THHTT,TTHHT,THTHT,HTHTT,TTHTH,TTTTH,TTTHT,TTHTT,THTTT,HTTTT,
TTTTT]
Sample space =28
E=2 heads at first two tosses =828
F=3 tails on next three tosses =428.
P(EF)=n(EF)n(F)
P(EF)=828428
=2.
n(F)=P(EF)no.oftosses
=25.
Hence, the answer is 25.

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