A coin is tossed n times. The probability of getting head at least once is greater than `0.8.` Then the least value of n is

Options

A. 2
B. 3
C. 5
D. 4

Answer

B

Explanation

let X be the number of heads getting in n tossed.
Therefore, X follows binomial distribution with parameters.
`n,p=(1)/(2),q=1/2`
Since , `P(X ge 1) ge 0.8" "` [given]
`therefore 1-P(X-0) ge 0.8`
`implies P(X=0) le 0.2`
`implies ""^(n)C_(0)((1)/(2))^(0)((1)/(2))^(n) le 0.2`
`implies (1)/(2^(n)) le (1)/(5)`
`implies 2^(n) ge 5`
Hence , least value of n is 3.