independent but not equally likely

mutually exclusive and independent

equally likely but not independent

equally likely and mutually exclusive

Statement I is incorrect, Statement II is correct

Statement I is correct, statement II is correct; Statement II is correct explanation for Statement I

Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I

Statement I is correct, Statement II is incorrect

JEE Questions for Maths Probability Quiz 4

Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is 6?

0%
5/36
0%
1/6
0%
2/15
0%
None of these

If three natural numbers from 1 to 100 are selected randomly, then probability that all are divisible by both 2 and 3, is

0%
4/105
0%
4/33
0%
4/35
0%
4/1155
0%
3/1155

The probability of getting a total of atleast 6 in the simultaneously throw of three dice is

0%
6/108
0%
5/27
0%
1/24
0%
103/108

0%
mutually exclusive and independent
0%
independent but not equally likely
0%
equally likely but not independent
0%
equally likely and mutually exclusive

The probability of simultaneous occurrence of atleast one of two events A and B is p. If the probability that exactly one of A , B occurs is q, then P (A' )+ P (B') is equal to

0%
2 - 2p + q
0%
2 + 2p - q
0%
3 - 3p + q
0%
2 - 4p + q

A and B are two events such that P(A) ≠ 0, then P(B/A )if
(i) A is a subset of B
(ii) A ∩ B = ∅

0%
1 and 1
0%
0 and 1
0%
0 and 0
0%
1 and 0

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is p,0< p< 1. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is

0%
0%
2)
0%
0%

A candidate takes three tests in succession and the probability of passing the first test is p. The probability of passing each succeeding test is p or p/2 according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, is

0%
p2 (2 - p)
0%
p(2 - p)
0%
p + p2 + p3
0%
p2(1 - p)

The probability of India winning a test match against South Africa is 1/2 assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is

0%
1/8
0%
1/2
0%
1/4
0%
2/3

If four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4 and 1/8. Then, the probability that the problem is solved correctly by atleast one of them, is

0%
235/256
0%
21/256
0%
3/256
0%
253/256

Of the three independent events E₁ , E₂ and E₃, the probability that only E₁ occurs is α, only E₂ occurs is β and E₁, E₂ or E₃ occurs satisfy the equations (α - 2β) p = αβ and (β - 3γ) p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1).

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

A box B₁ contains 1 white ball, 3 red balls and 2 black balls. Another box B₂ contains 2 white balls, .3 red balls and 4 black balls. A third box B₃ contains 3 white balls, 4 red balls and 5 black balls.
If 1 ball is drawn from each of the boxes B₁, B₂ and B₃ ,the probability that all 3 drawn balls are of the same colour, is

0%
82/648
0%
90/648
0%
558/648
0%
566/648

A ship is fitted with three engines E₁ , E₂ and E₃. The engines function independently of each other with respective probabilities 1/2, 1/4 and 1/4. For the ship to be operational atleast two of its engines must function. Let X denotes the event that the ship is operational and let X₁ , X ₂ and X₂ denote, respectively the events that the engines E₁ , E₂ and E₃ are functioning. Which of the following is/are correct?

0%
0%
P(excatly two engines of the ship are functioning x = 7/8)
0%
0%

If X and Y are two events that P(X ∕ Y ) = 1/2, P(Y ∕ X) = 1/3 and P(X ∩ Y) = 1/6, then which of the following is/are correct?

0%
P(X ∪ Y) = 2/3
0%
X and Y are independent
0%
X and Y are not independent
0%
P(Xc ∩ Y) = 1/3

A and B throw a dice alternatively till one of them gets a six and wins the game. If A starts the game first, then the probability of A wining the game is

0%
3/11
0%
5/11
0%
6/11
0%
7/11

Three numbers are chosen at random without replacement from {1, 2, ...8}. The probability that their minimum is 3, given that their maximum is 6, is

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

Let U₁ and U₂, be two urns such that U₁ contains 3 white and 2 red balls and U₂, contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears, then 2 balls are drawn at random from U₁ and put into U₂. Now, 1 ball is drawn at random from U₂.
22. The probability of the drawn ball from U₂ being white

0%
13/30
0%
23/30
0%
19/30
0%
11/30

Let U₁ and U₂, be two urns such that U₁ contains 3 white and 2 red balls and U₂, contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears, then 2 balls are drawn at random from U₁ and put into U₂. Now, 1 ball is drawn at random from U₂.
If the drawn ball from U₂ is white, then the probability that head appeared on the coin is

0%
17/23
0%
11/23
0%
15/23
0%
12/23

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then

0%
P(E) = 4/5, P(F) = 3/5
0%
P(E) = 1/5, P(F) = 2/5
0%
P(E) = 2/5, P(F) = 1/5
0%
P(E) = 3/5, P(F) = 4/5

If A, B and C are pairwise independent events with P(C) > 0 and P(A ∩ B ∩ C) = 0. Then, P(A^c ∩ B^c ∕ C) is equal to

0%
P(Ac) - P(B)
0%
P(A) - P(Bc)
0%
P(Ac) + P(Bc)
0%
P(Ac) - P(Bc)

If A and B are two non-empty sets with B^c denoting the complement of set B such that B ⊂ A, then which of the following probability statements hold correct?

0%
P(A ∩ Bc) = P(B) - P(A)
0%
P(A ∩ Bc) = P(A) - P(B)
0%
P(B) ≤ P(A)
0%
P(A) ≤ P(B)

A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal green is

0%
3/5
0%
6/7
0%
20/23
0%
9/20

Two dice are tossed once. The probability of getting even number at the first die or a total of 8 is

0%
1/36
0%
3/36
0%
11/36
0%
5/9

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero equals

0%
1/14
0%
1/7
0%
5/14
0%
1/50

An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed, is

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

The probability that in the toss of two dice, we obtain an even sum or a sum less than 5 is

0%
1/2
0%
1/6
0%
2/3
0%
5/9

If A and B are two independent events such that P(A ∪ B') = 1 and P(A) = 0.3. Then, P(B) is equal to

0%
2/7
0%
2/3
0%
3/8
0%
1/8

A and B toss a coin alternately on the understanding that the first to obtain head win the toss. The probability that A wins the toss, is

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

In tossing of a coin (m + n) (m> n) times, the probability of coming consecutive heads atleast m times is

0%
0%
2)
0%
0%

0%
A = 2, B = 3, C = 4, D = 1
0%
A = 4, B = 5, C = 6, D = 1
0%
A = 4, B = 2, C = 6, D = 1
0%
A = 1, B = 2, C = 3, D = 4

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is euqal to

0%
2, 4 or 8
0%
3, 6 or 9
0%
4 or 8
0%
5 or 10

It is given that the events A and B are such that P(A) = 1/4, P(A/B) = 1/2 and P(B/A) = 2/3. Then, P(B) is equal to

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

A die is thrown. If A is the event that the number obtained is greater than 3 and B is the event that the number obtained is less than 5. Then, P(A ∪ B) is

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

If A and B are any two events, then P(A ∩ B') is equal to

0%
P(A) + P(B')
0%
P(A)P(B)
0%
P(B) - P(A ∩ B)
0%
P(A) - P(A ∩ B)
0%
1 - P(A ∩ B)

If E₁ and E₂ are two mutually exclusive events of an experiment with P (not E₂) = 0.6 = P(E₁ ∪ E₂). Then, P(E₁) is equal to

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

0%
Statement I is correct, statement II is correct; Statement II is correct explanation for Statement I
0%
Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I
0%
Statement I is correct, Statement II is incorrect
0%
Statement I is incorrect, Statement II is correct

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

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

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is

0%
0.06
0%
0.14
0%
0.32
0%
0.7

If P(A) = 1/12, P(B) = 5/12 and P(B/A) = 1/15, then P(A ∪ B) is equal to

0%
89/180
0%
90/180
0%
91/180
0%
92/180

An urn contains 3 red and 5 blue balls. The probability that two balls are drawn in without replacement is

0%
5/16
0%
5/56
0%
5/8
0%
20/56

0%
0%
2)
0%
0%

Seven chits are numbered 1 to 7. Four chits are drawn one by one with replacement. The probability that the least number appearing on any selected chit is 5, is

0%
0%
2)
0%
0%

An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1st, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1, respectively. What is the probability that atleast one shot hits the plane?

0%
0.6976
0%
0.3024
0%
0.72
0%
0.6431
0%
0.7391

An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8, is

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

A fair die is rolled. The probability that the first time 1 occurs at the even throw is

0%
1/6
0%
5/11
0%
6/11
0%
5/36

If A, B are two events and P(A') = 0.3, P(B) = 0.4 and P(A ∩ B') = 0.5, then P(A ∪ B') is equal to

0%
0.5
0%
0.8
0%
1
0%
0.1

Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box, then the probability that it has come from box B, is