Probability Test

Result

Probability Test - 26

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Weekly Quiz Competition

Question 1
4 / -1

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 = ∅

A
1 and 1

B
0 and 1

C
0 and 0

D
1 and 0

Solution
Question 2
4 / -1

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

A

B

C

D
Question 3
4 / -1

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

A
p² (2 - p)

B
p(2 - p)

C
p + p² + p³

D
p²(1 - p)
Question 4
4 / -1

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

A
1/8

B
1/2

C
1/4

D
2/3
Question 5
4 / -1

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

A
235/256

B
21/256

C
3/256

D
253/256
Question 6
4 / -1

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).

A
6/1

B
1/3

C
1/2

D
1/4
Question 7
4 / -1

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

A
82/648

B
90/648

C
558/648

D
566/648
Question 8
4 / -1

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?

A

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

C

D
Question 9
4 / -1

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?

A
P(X ∪ Y) = 2/3

B
X and Y are independent

C
X and Y are not independent

D
P(X^c ∩ Y) = 1/3

Solution
Question 10
4 / -1

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

A
3/11

B
5/11

C
6/11

D
7/11

Solution