If a fair coin is tossed 5 times, the porbability that heads does not occur two or more times in a row is

Options

A. `(12)/(2^(5))`
B. `(13)/(2^(5))`
C. `(14)/(2^(5))`
D. `(15)/(2^(5))`

Answer

B

Explanation

Case (1): All tail `((1)/(2))^(5)`
Case(2): 4T,1H `""^(5)C_(4)((1)/(2))^(4).((1)/(2))^(5)=(5)/(2^(5))`
Case (3): `xxTxxTxxTxx`
`((1)/(2))^(3)xx""^(4)C_(2)xx((1)/(2))^(2)=(1)/(2^(5))xx6=(6)/(2^(5))`
Case (4),`xxTxxTxx`
`((1)/(2))^(2)xx((1)/(3))^(3)=(1)/(2^(5))`
overall `(13)/(2^(5))`