Question

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`

Answer 1

Correct Answer - D
Let `H_i` denote the event of getting a head in `i^th` toss and `T_(i)` denote the event of getting a tail in `i^th` toss. Then, Required probability.
`=P{(H_1capH_2capH_3capH_4capT_5)cup (T_1capT_2capT_3capT_4capH_5)}`
`=P(H_1cap H_2cap H_3capH_4capT_5)+P(T_1cap T_2cap T_3capT_4cap cap H_5)`
`=P(H_1)P(H_2)P(H_3)P(H_4)P(T_5)+P(T_1)P(T_2)P(T_3)P(T_4)P(H_5)`
`-((1)/(2))^5+((1)/(2))^5=(1)/(16)`