A man throws a fair coin number of times and gets 2 points for each head and 1 point for each tail the probability that he gets exactly 6 points is `(21)/(32)` (2) `(13)/(64)` (3) `(43)/(64)` (4) `(23)/(32)`

Options

A. `21/32`
B. `23/32`
C. `41/64`
D. `43/64`

Answer

D

Explanation

`P("HHH")+P("HHTT") + P("HTTTT") + P("TTTTTT")`
`1/(2^(3)) + .^(4)C_(2) (1)/(2^(4)) + .^(5)C_(1) (1)/(2^(5))+(1)/(2^(6))`
`= 1/(8) + (6)/(16) + (5)/(32) + (1)/(64)`
`= 43/64`