Q. 1065.0( 1 Vote )

Fill in the blanks in the following question:

If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9.P (X = 3), then p = ___________

Answer :

p = 1/10

As n = 5 {representing no. of trials}


p = probability of success


As it is a binomial distribution.


probability of failure = q = 1 – p


Given,


P(X = 2) = 9.P(X = 3)


The binomial distribution formula is:


P(x) = nCx Px (1 – P)n – x


Where:


x = total number of “successes.”


P = probability of success on an individual trial


n = number of trials


Using binomial distribution,


5C2p2q5-2 = 95C3p3q5-3


10p2q3 = 9×10p3q2


10q = 90p {As , p≠0 and q ≠ 0}


q = 9p


1-p = 9p 10p = 1


p = 1/10


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