The probability that a student is not a swimmer is . Then the probability that out of five students, four are swimmers is (A) (B) (C) (D) None of these
It is given that 1 5 is the probability that a student is not a swimmer.
Let the number of students who are swimmer from a sample space of 5 is represented by X.
The probability of students who are not swimmer is,
q = 1 5
So,
p = 1 − q = 1 − 1 5 = 4 5
Then X has a binomial distribution with n = 5 and p = 4 5 .
The probability of x successes P ( X = x ) is,
P ( X = x ) = C n x q n − x p x = C 5 x ( 1 5 ) 5 − x ( 4 5 ) x
Where, x = 0 , 1 , … , n .
The probability that 4 students are swimmer is,
P ( X = 4 ) = C 5 4 ( 1 5 ) 1 ( 4 5 ) 4 = C 5 4 ( 4 5 ) 4 ( 1 5 )
Therefore, option (A) is correct.
It is given that
Let the number of students who are swimmer from a sample space of 5 is represented by X.
The probability of students who are not swimmer is,
So,
Then X has a binomial distribution with
The probability of
Where,
The probability that 4 students are swimmer is,
Therefore, option (A) is correct.
