RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 33. Binomial Distribution

Subject: Maths - Class 12th

Q. No. 12 of Very Short Answer

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12

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

Given:


n=5


p(x=2)=9p(x=3)


p=?


P(x=r)= nCr pr qn-r


P(x=1)= 5C1 p1 q4


= 5p q4


P(x=3)= 5C3 p3 q2


= 20 p3 q2


Put values in equation, we have:


5p q4= 9(20 p3 q2)


q2= 9(4 p2)


(1-p)2= 36p2


1+p2-2p= 36p2


35p2+2p-1=0



Chapter Exercises

Exercise 33.2
Exercise 33.1
Very Short Answer
MCQ

More Exercise Questions

1

In a binomial distribution, if n = 20, q = 0.75, then write its mean.
2

If in a binomial distribution mean is 5 and variance is 4, write the number of trials.
3

In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.
4

If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
5

The mean of a binomial distribution is 10 and its standard deviation is 2, write the value of q.
6

If the mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, find P (X = 1).
7

If the mean and variance of a binomial variate X are 2 and 1 respectively, find P(X > 1).
8

If in a binomial distribution n = 4 and find q.
9

If the mean and variance of a binomial distribution are 4 and 3 respectively, find the probability of no-success.
10

If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X= 4) in terms of α.
11

An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
12

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

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