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A fair coin is tossed n times. if the pr...

A fair coin is tossed `n` times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value of `ndot`

A

7

B

14

C

16

D

19

Text Solution

Verified by Experts

The correct Answer is:
B
let X denotes the number of heads in heads in n trials . Then, X is a binomial variate with `p=q=1/2`
`therefore P(X=r) = ""^(n)C_(r)(1/2)^(n)`
`because P(X=6)=P(X=8)implies ""^(n)C_(6)(1/2)^(n)=""^(n)C_(8)(1/2)^(n)`
`implies ""^(n)C_(6)=""^(n)C_(8)implies n=14`
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Knowledge Check

  • A fair coin is tossed 100 times.The probability of getting head an odd number of times is

    A
    `1/4`
    B
    `2/3`
    C
    `1/2`
    D
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  • A coin is tossed four times. The probability that atleast one heads turns up is

    A
    `(1)/(16)`
    B
    `(1)/(8)`
    C
    `(7)/(8)`
    D
    `(15)/(16)`

  • A fair coin is tossed 9 times the probability that at least 5 consecutive heads occurs is :

    A
    `5/64`
    B
    `3/32`
    C
    `""^9C_5 (1/2)^9`
    D
    None of these

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