Test: Probability And Statistics - 4


20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Test: Probability And Statistics - 4


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QUESTION: 1

The probability that a number in {1, 2,..., 1001} is divisible by 7 or 11 or both, is

Solution:

Number of integers divisible by 7 

Number of integers divisible by 11

Number of integers divisible by both 7 and 11

Required probability of = 221/1001 Ans.

QUESTION: 2

 If A and B are two events, the probability that exactly one of them occurs is

Solution:


Prob. that exactly one of them occurs

QUESTION: 3

A number is chosen from each of the two sets {1 , 2 , 3, 4, 5, 6 , 7. 8 , 9} and {1, 2 . 3, 4, 5, 6 , 7, 8 , 9}. If pdenotes the probability that the sum of the two numbers be 10 and pthe probability that their sum be 8, then (p1 + p2] is

Solution:

Sum is 10 if 1 + 9, 2 + 8,...9 + 1 is taken 9 cases.
sum is 8 if 1 + 7, 2 + 6,...7 + 1 is laken 7 cases.

QUESTION: 4

The probability that a non-leap year should have 53 Sunday is

Solution:

If year starts with Sunday it will end on Sunday, but year can start on any one of 7 days
Hence prob. = 1/7

QUESTION: 5

A coin is biased so that the probability of head = 1/4. The coin is tossed five times. The probability of obtaining two heads and three tails with heads occurring in succession is

Solution:


Two consecutive head can appear in 4 ways remaining places goes to tail, so require probability is

QUESTION: 6

15 coupons are numbered 1,2 ..... 15. Seven coupons are selected at random, one at a time, with replacement. The probability that the largest number appearing on a selected coupon is 9, is

Solution:

  ; as numbers from 1 to 9 is selected 7 times and we subtract the case in which number 1 to 8 is selected all 7 times. 

QUESTION: 7

Let A and B be any two arbitrary’ events, then, which of the following is true?

Solution:


⇒ 

QUESTION: 8

A die is loaded in such a way that each odd number is twice as likely to occur as each even number. If E is the event that a number greater than or equal to 4 occurs on a single toss of the die, then P (E) is

Solution:

Let probability of occurence of even number be k, then probability of occurence of odd number will be 2 k.

QUESTION: 9

The probability that a person tossing three fair coins will get together all heads or all tails for the second time on the 5th toss is

Solution:

QUESTION: 10

The probabilities that three men hit a target are 1/6, 1/4, 1/3 respectively. Each shoots once the target. What is the probability that exactly one of them hits the target?

Solution:

QUESTION: 11

Let X, Y. Z be three independent normal variables N(0, 1). Then E(X - Y + Z)2] is

Solution:


As, x, y, z are independent.
= 1 + 1 + 1 + 0 + 0 + 0 = 3

QUESTION: 12

A probability distribution must possess

Solution:

Every probability distribution possess distribution function but mean, mode and moment generaLinig function may not exist.

QUESTION: 13

In a Poisson distribution

Solution:

R.V.X follows poisson distribution if

QUESTION: 14

For a frequency distribution of marks in Mathematics for 100 students, the average was found to be 80. Later on it was discovered that. 4 8 was misread as 84. The correct mean is

Solution:

QUESTION: 15

For a binomial distribution, the mean is (15/4) and the variance is (15/16). The value of p is

Solution:


QUESTION: 16

Following is the distribution of marks in Statistics obtained by 50 students :

If 60% of students passes the test, then what is the minimum marks obtained by a candidate who has passed?

Solution:


60 % students have passed, so 50 x 60% = 30 students have passed.
Total 30 students fall in class 20 - 30 whose mid value is  Hence answer is 25.

QUESTION: 17

Telephone calls come into an exchange according to a Poisson process with 5 calls per minute on the average. The probability that no call will come in during the two minute period 10 A.M. to 10:02 A.M. on a particular day is

Solution:

QUESTION: 18

The coefficient of correlation between X and Y for the following bivariate distribution is

Solution:



= -4/5

QUESTION: 19

X1, X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) is

Solution:

[F(x)]n

QUESTION: 20

Telephone calls come into an exchange according to a Poisson process with 5 calls per minute on the average. The probability that no call will come in during the two-minute period 10 A.M. to 10:02 A.M. on a particular day is

Solution:

λ = 5 x 2 = 10

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