A coin is tossed 6 times . Find the probability of getting at least 3 heads .

Options

A. `(11)/( 16)`
B. `(21)/(32)`
C. `(1)/(18)`
D. `(3)/(64)`

Answer

B

Explanation

In a single throw we have `P(H) =(1)/(2) ` and P (not H) =`(1)/(2)`
`:. , p =(1)/(2),q=(1)/(2) " and " n=6`
Required probability =P(3 heads or 4 heads or 5 heads or 6 heads )
`=^(6)C_(3) .((1)/(2))^(3).((1)/(2))^(3)+.^(6)C_(4) .((1)/(2))^(4) .((1)/(2))^(2) +.^(6)C_(5).((1)/(2))^(5).((1)/(2)) +.^(6)C_(6).((1)/(2))^(6)`
`=(20 xx (1)/(64) +15 xx (1)/(64) +6xx (1)/(64) +(1)/(64)) =(42)/(64) =(21)/(32)`