Question

If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes values at most 3 is

Solution

Correct option is

15/16

 

We have E(X) = np = 2 and var (X) = npq = 1. Therefore, q = 1/2 or p = 1/2, and n = 4. Thus,

                    

SIMILAR QUESTIONS

Q1

For the three events AB and CP(exactly one of the events A or Boccurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p2, where 0 < p < 1/2. Then the probability of at least one of the three events AB and C occurring is

Q2

Nine identical balls are numbers 1, 2,…9. Are put in a bag. A draws a ball and gets the number a. the ball is put back the beg. Next B draws a ball gets the number b. The probability that a and b satisfies the inequality a – 2b + 10 > 0 is

Q3

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is then,

Q4

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

Q5

Let ABC, be three mutually independent events. Consider the two statements S1 and S2.

                        S1 : A and B ∪ C are independent

                        S2 : A and B ∩ C are independent

Then

Q6

If m is a natural such that m ≤ 5, then the probability that the quadratic that the quadratic equation x2 + mx +  has real roots is

Q7

There are m persons setting in a row. Tow of then the selected at random. The probability that the two selected person are not together is

Q8

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A’) + P(B’) is

Q9

Three six – faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is 

k (3 ≤ k ≤ 8) is

Q10

If two events A and B such that P(A’) = 0.3, P(B) = 0.5 and P(A  B) = 0.3, then  is