If the mean and the variance of a binomi...

If the mean and the variance of a binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to:

Text Solution

Verified by Experts

The correct Answer is:

For Biomial distribution, mean =np
and variance=npq
`:. " "np=2 " "and " "npq=1" "` [given]
`rArr " "q=1//2 " and "p+q=1`
`rArr " "p=1//2`
`:. " "n=4,p=q=1//2`
Now, `P(X gt1)=1-{P(X=0)+P(X=1)}`
`=1-overset(4)C_(0)((1)/(2))^(0)((1)/(4))^(4)-overset(4)""C_(1)((1)/(2))^(1)((1)/(2))^(3)`
`=1=-(1)/(16)-(4)/(16)=(11)/(16)`

Topper's Solved these Questions

PROBABILITY
IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 PROBABILITY DISTRIBUTION AND BINOMIAL DISTRIBUTTION OBJECTIVE QUESTIONS ONLY ONE CORRECT OPTION (ANALYTICAL & DESCRIPTIVE QUESTIONS )|4 Videos
PROBABILITY
IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 PROBABILITY DISTRIBUTION AND BINOMIAL DISTRIBUTTION OBJECTIVE QUESTIONS ONLY ONE CORRECT OPTION (INTEGER )|1 Videos
PROBABILITY
IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 PROBABILITY DISTRIBUTION AND BINOMIAL DISTRIBUTTION OBJECTIVE QUESTIONS (ONLY ONE CORRECT OPTION)|11 Videos
PERMUTATIONS AND COMBINATIONS
IIT JEE PREVIOUS YEAR|Exercise Dearrangement and Number of Divisors (Fill in the Blank )|1 Videos
RELATIONS AND FUNCTIONS
IIT JEE PREVIOUS YEAR|Exercise All Questions|1 Videos

If the mean and variance of a binomial variate X are α and 1 respectively, then the probability that X takes a value greater than one equal to

`13//16`

`12//16`

`9//16`

`11//16`

If mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is:

A) `(2)/(3)`

B) `(4)/(5)`

C) `(7)/(8)`

D) `(11)/(16)`

The mean and variance of a binomial variable X are 2 and 1, respectively. The probability that X takes values greater than 1, is

`(5)/(16)`

`(8)/(16)`

`(11)/(16)`

`(1)/(16)`