Q1.

In a non-leap year, the probability of getting 53 Mondays or 53 Wednesdays or 53 Fridays is 

  • 3/7

  • 1/7

  • 2/7

  • 4/7

Solution:

3/7

Q2.

If E(x) = 3, Find the value of E(3x + 3)

  • 11

  • 12

  • 14

  • 16

Solution:

12

Q3.

One card is drawn from the pack of 52 cards, what is the probability that it is a King or Ace ?

  • 2/13

  • 3/13

  • 4/13

  • 1/2

Solution:

2/13

Q4.

If 10 men among whom P and Q stand in a row, what is the probability that there will be exactly 3 men between P and Q ?

  • 1/20

  • 2/15

  • 9/10

  • 3/4

Solution:

2/15

Q5.

If A and B are two events and P(A) = 3/8, P(B) = 1/2, P(A and B) = 1/4,  then find the value of P(A' and B')

  • 3/7

  • 4/9

  • 3/8

  • 1/4

Solution:

3/8

Q6.

From the well suffuled pack of cards, two cards are drawn, the first being replaced before the second is drawn. The chance that the first is a club and the second is jack is 

  • 2/13

  • 2/19

  • 1/4

  • 1/52

Solution:

1/52

Q7.

A person plays a game of tossing a dice. If the number less three appears he is getting Rs. x, otherwise he has to pay Rs. 10. Game is fair find x ?

  • 12

  • 22

  • 30

  • 20

Solution:

20

Q8.

The odds are 5 : 9 in favour a person who is 80 years living till he is 100 and 8 : 6 against a person who is 90 living till he is 110. Find the probability that atleast one of them will be alive after 20 years. 

  • 31/49

  • 32/49

  • 23/36

  • 0.43

Solution:

31/49

Q9.

An urn contains 6 red and 4 green balls. 3 balls are drawn without replacement. Find E(x) of green balls that will be obtained ?

  • 0.4

  • 1.5

  • 1.8

  • 1.2

Solution:

1.2

Q10.

Which statement is false?

(a). If P(A and B) = P(A). P(B) , then A and B are independent events

(b). E(XY) = E(X). E(Y)

(c). V(K) = 0, where k is an constant

(d). V(ax) = a.V(x)

  • a

  • b

  • c

  • d

Solution:

d

Q11.

Which statement is wrong ?

(a). Normal distribution is continous bi-parametic distribution.

(b). In poisson  distribution mean = variance.

(c). Binomial distribution is a univariate distribution.

(d). Normal distribution is a bell shape distribution.

  • a

  • b

  • c

  • d

Solution:

c

Q12.

If the mean of a poisson variable X is 1, what is P( x = at least one) ?

  • 0.734

  • 0.446

  • 0.365

  • 0.632

Solution:

0.632

Q13.

In a poisson distribution P(X = 0) = P(X = 2), find V(X).

  • 2

  • 3

  • 4

  • \( { \sqrt{2} \ }\)

Solution:

\( { \sqrt{2} \ }\)

Q14.

For binomial distribution E(X) = 3 and V(X) = 9/4, find n.

  • 12

  • 11

  • 45

  • 6

Solution:

12

Q15.

In a poisson distribution standard deviation is 3, find the mode/s ?

  • 8

  • 9

  • 2 and 3

  • 8 and 9

Solution:

8 and 9

Q16.

The point of inflexion of a normal distribution are 8 and 6, find median.

  • 1

  • 7

  • 6

  • 3

Solution:

7

Q17.

Which statement is wrong ?

(a). In poisson distribution the probability of success is very very small.

(b). Variance of standard normal variate is 1.

(c). The area under the normal curve is 1.

(d). Binomial is unimodal distribution.

  • a

  • b

  • c

  • d

Solution:

d

Q18.

In a normal Distribution Quartile Deviation is 6, S.D. will be.

  • 5

  • 7

  • 9

  • 8

Solution:

9

Q19.

If the mean and the variance of a binomial distribution are 4 and 4/3, then find P(x \(\geq\) 1).

  • 728/729

  • 700/729

  • 728/600

  • none of these 

Solution:

NA

Q20.

In a binomial distribution , the sum of its mean and variance is 1.8. Find the probabaility of two successes if the event was conducted 5 times . 

  • 0.2046

  • 0.2048

  • 0.1048

  • 0.2044

Solution:

NA