JEE Questions for Maths Probability Quiz 2

If A and B are two events with P(A^c) = 0.3, P(B) = 0.4 and P(A ∩ B^c) = 0.5. Then, P[(B) ∕ (A ∩ B^c)] is equal to

0%
1/4
0%
1/3
0%
1/2
0%
2/3

If n positive integers are taken at random and multiplied together, then the probability that the last digit of the product is 2, 4, 6 or 8, is

0%
0%
2)
0%
0%
None of these

let A, B and C be the three events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A ∩ B) = 0.08 P(A ∩ C) = 0.28 and P(A ∩ B ∩ C) = 0.09. If P(A ∪ B ∪ C) ≥ 0.75, then P(B ∩ C) satisfies

0%
P(B ∩ C) ≤ 0.23
0%
P(B ∩ C) ≤ 0.48
0%
0.23 ≤ P(B ∩ C) ≤ 0.48
0%
0.23 ≤ P(B ∩ C) ≥ 0.48

A bag contains a white and b black balls. Two players A and B alternately draw a ball from the bag replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, then the ratio a : b is

0%
1 : 1
0%
1 : 2
0%
2 : 1
0%
None of these

If P(A ∪ B) = 0.6 and P(A ∩ B) = 0.2, then the probability of exactly one of the event occurs is

0%
0.4
0%
0.2
0%
0.6
0%
0.8

If P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.3, then P(A'/B') is equal to

0%
1/3
0%
1/2
0%
2/3
0%
3/4

0%
1/3
0%
1/4
0%
1/2
0%
2/3

A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail the first two times is

0%
9/64
0%
1/64
0%
1/16
0%
9/16

0%
9/10
0%
8/10
0%
7/10
0%
3/5

A man is known to speak the truth 3 out of 4 times. He throws a die arid reports that it is six. The probability that it

0%
3/8
0%
1/5
0%
3/4
0%
None of these

0%
1/4
0%
1/3
0%
5/7
0%
2/3

The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday is

0%
3/7
0%
2/7
0%
5/7
0%
1/7

The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in atleast one subject?

0%
28%
0%
38%
0%
72%
0%
82%

A parents has two children. If one of them is boy, then the probability that other is also a boy, is

0%
1/2
0%
1/4
0%
1/3
0%
None of these

A person draws out two balls successively from a bag containing 6 red and 4 white balls. The probability that atleast one of them will be red, is

0%
78/90
0%
30/90
0%
48/90
0%
12/90

0%
5/12
0%
3/8
0%
5/8
0%
1/2

For k = 1, 2, 3 the box B_k contains k red balls and (k +white balls. Let P(B₁) = 1/2, P(B₂) = 1/3 and P(B₃) = 1/6, A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box B₂, is

0%
35/78
0%
14/39
0%
10/13
0%
12/13

If A and B are two independent events such that P(B) = 2/7, P(A ∪ B^c) = 0.8, then P(A) is equal to

0%
0.1
0%
0.2
0%
0.3
0%
0.4

For two events A and B, if P(A) = P(A/B) = 1/4 and P(B?A) = 1/2, then

0%
A and B are independent events
0%
P(A'/B) = 3/4
0%
P(B'/A) = 1/2
0%
All of the above

If P(A) = P(B) = x and P(A ∩ B) = P(A' ∩ B') = 1/3, then x is equal to

0%
1/2
0%
1/3
0%
1/4
0%
1/6

The probability that atleast one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then

0%
0.4
0%
0.8
0%
1.2
0%
1.4

0%
0%
2)
0%
0%

If A and B are mutually exclusive with P(A) = (1/× P(B) and A ∪ B = S(total sample space), then P(A) is equal to

0%
2/3
0%
1/3
0%
1/4
0%
3/4

X speaks truth in 60% and Y in 50% of the cases. The probability that they contradict each other narrating the same incident is

0%
1/4
0%
1/3
0%
1/2
0%
2/3

A bag contains 3 black, 3 white and 2 red balls. One by one, three balls are drawn without replacement. The probability that the third ball is red, is

0%
2/56
0%
3/56
0%
1/56
0%
12/56
0%
14/56

0%
1/12
0%
1/6
0%
1/15
0%
1/9

The probability that in the toss of two dice, we obtain the sum 7 or 11 is

0%
1/6
0%
1/18
0%
2/9
0%
23/108

If the probability of A to fail in an examination is 0.2 and that for B is 0.3, then probability that either A or B is fail, is

0%
0.5
0%
0.44
0%
0.8
0%
0.25

A bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted to be green. The probability that it comes from bag B is

0%
2/7
0%
2/3
0%
3/7
0%
1/3

A bag contains 5 white and 3 black balls and 4 balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is

0%
1/196
0%
2/7
0%
1/7
0%
13/56

If events are independents and P(A) = 1/3, P(B) = 1/3 and P(C) = 1/4, then P(A' ∩ B' ∩ C') is equal to

0%
1/4
0%
1/12
0%
1/3
0%
5/12

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second, is

0%
1/2
0%
3/4
0%
7/18
0%
5/12

A biased coin with probability p, 0 < p < 1 of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2 / 5, then p equals

0%
1/3
0%
2/3
0%
2/5
0%
3/5

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is

0%
1/2
0%
3/4
0%
1/4
0%
2/3

If A and B are two independent events such that P(A) = 1/2 and P(B) = 1/3, then P(neither A nor B) is equal to

0%
2/3
0%
1/6
0%
5/6
0%
1/3

If E and F are two independent events such that 0 < P(E) < 1 and 0 < P(F) < 1, then

0%
E and Fc are independent
0%
Ec and Fc are independent
0%
0%
None of the above

If X denotes the sum of the numbers obtained when two fair dice are rolled, then the variance and standard deviation of X are

0%
0%
2)
0%
0%

If the mean and variance of a Binomial variate X are 8 and 4 respectively, then P(X

0%
265/215
0%
137/214
0%
137/16
0%
265/216

0%
16/3
0%
4/3
0%
5/3
0%
10/3

If the mean and variance of a random variable X having a Binomial distribution are 4 and 2 respectively, then find the value of P(X =1).

0%
1/4
0%
1/16
0%
1/8
0%
1/32

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

0%
17/35
0%
13/35
0%
11/35
0%
10/35

Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of atleast one failure is greater than or equal to 31/2, the p lies in the interval

0%
0%
2)
0%
0%

0%
0.77
0%
0.87
0%
0.35
0%
0.50

Two dice are thrown n times in succession. The probability of obtaining a double six atleast once is

0%
0%
2)
0%
0%
None of these

If X is a Binomial variate with the range {0, 1, 2, 3, 4, 5, 6} and P(X == 4P(X = 4), then the parameter p of X is

0%
1/3
0%
1/2
0%
2/3
0%
3/4

If a fair coin is tossed 20 times and we get head n times, then probability that n is odd, is

0%
1/2
0%
1/6
0%
5/8
0%
7/8

A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ, is