Un biased coin is tossed 6 times. The probability of getting atmost 4 heads is

Options

A. `(7)/(64)`
B. `(57)/(64)`
C. `(21)/(32)`
D. `(11)/(32)`

Answer

B

Explanation

Probability of gettting head `p=(1)/(2) ` and tail `=1/2`
Here n=6
`therefore P (X =x)=""^(6)C_(x) ((1)/(2))^(6)`
`+(x le 4)=1-P(x gt 4)=1-""^(5)C_(5)((1)/(2))^(5)((1)/(2))^(1)-""^(6)C_(6)((1)/(2))^(6)`
`=1-(""^(6)C_(5))/(2^(6))-(1)/(2^(6))=(57)/(64)`