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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The probability that a number in {1, 2,..., 1001} is divisible by 7 or 11 or both, is
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.
If A and B are two events, the probability that exactly one of them occurs is
Prob. that exactly one of them occurs
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 p1 denotes the probability that the sum of the two numbers be 10 and p2 the probability that their sum be 8, then (p1 + p2] is
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.
The probability that a non-leap year should have 53 Sunday is
If year starts with Sunday it will end on Sunday, but year can start on any one of 7 days
Hence prob. = 1/7
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
Two consecutive head can appear in 4 ways remaining places goes to tail, so require probability is
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
; 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.
Let A and B be any two arbitrary’ events, then, which of the following is true?
⇒ 
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
Let probability of occurence of even number be k, then probability of occurence of odd number will be 2 k.
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
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?
Let X, Y. Z be three independent normal variables N(0, 1). Then E(X - Y + Z)2] is
As, x, y, z are independent.
= 1 + 1 + 1 + 0 + 0 + 0 = 3
Every probability distribution possess distribution function but mean, mode and moment generaLinig function may not exist.
R.V.X follows poisson distribution if
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
For a binomial distribution, the mean is (15/4) and the variance is (15/16). The value of p is
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?
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.
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
The coefficient of correlation between X and Y for the following bivariate distribution is
= -4/5
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
[F(x)]n
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
λ = 5 x 2 = 10
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