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A fair coin is tossed repeatedly. The probability of getting a result in fifth toss different from those obtained in the first four tosses is

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A fair coin is tossed repeatedly. The probability of getting a result in fifth toss different from those obtained in the first four tosses is A. 1 2 B. 1 32 C. 31 32 D. 1 16 Select the correct answer from above options

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Correct Answer - D Let Hi denote the event of getting a head in ith toss and Ti denote the event of getting a tail in ith toss. Then, Required probability =P{(H1∩H2∩H3∩H4∩T5∪(T1∩T2∩T3∩T4∩T5)} =P(H1∩H2∩H3∩H4∩T5)+P(T1∩T2∩T3∩T4∩T5) =P(H1)P(H2)P(H3)P(H4)P(H5)+P(T1)P(T2)P(T3)P(T4)P(H5) =( 1 2 )5+( 1 2 )5= 1 16

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