Question 1.
If A and B are two independent events, then
(a) P(A∩B) = P(a) × P(b)
(b) P(AB) = 1 – P(A’) P(B’)
(c) P(AB) = 1 + P (A’) P(B’) P(A’)
(d) P (AB) = \(\frac{P(A’)}{P(B’)}\)

Answer

Answer: (a) P(A∩B) = P(a) × P(b)

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Question 2.
The probability of an event is \(\frac{3}{7}\). Then odd against the event is
(a) 4 : 3
(b) 7 : 3
(c) 3 : 7
(d) 3 : 4

Answer

Answer: (a) 4 : 3

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Question 3.
A pair of dice are rolled. The probability of obtaining an even prime number on each die is
(a) \(\frac{1}{36}\)
(b) \(\frac{1}{12}\)
(c) \(\frac{1}{6}\)
(d) 0

Answer

Answer: (a) \(\frac{1}{36}\)

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Question 4
If P(a) = \(\frac{3}{8}\), P(b) = \(\frac{1}{3}\) and P(A∩B) = — then P (A’ ∩B’)
(a) \(\frac{13}{24}\)
(b) \(\frac{13}{8}\)
(c) \(\frac{13}{9}\)
(d) \(\frac{13}{4}\)

Answer

Answer: (a) \(\frac{13}{24}\)

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Question 5.
P(A∩B) = \(\frac{3}{8}\), P(b) = \(\frac{1}{2}\) and P(a) = \(\frac{1}{4}\) then P(\(\frac{B’}{A’}\)) =
(a) \(\frac{3}{5}\)
(b) \(\frac{5}{8}\)
(c) \(\frac{3}{8}\)
(d) \(\frac{5}{6}\)

Answer

Answer: (d) \(\frac{5}{6}\)

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Question 6.
If A and B are two events such that P(a) ≠ 0 and P(\(\frac{B}{A}\)) = 1 then
(a) P(\(\frac{A}{B}\)) = 1
(b) P(\(\frac{B}{A}\)) = 1
(c) P(\(\frac{A}{B}\)) = 0
(d) P(\(\frac{B}{A}\)) = 0

Answer

Answer: (b) P(\(\frac{B}{A}\)) = 1

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Question 7.
If P (a) = \(\frac{3}{8}\), P(b) = \(\frac{1}{2}\) and P(A∩B) = \(\frac{1}{4}\) then P(\(\frac{A’}{B’}\)) =
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{3}{4}\)
(d) \(\frac{3}{8}\)

Answer

Answer: (b) \(\frac{1}{3}\)

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Question 8.
If A and B are two events such that P(a) ≠ 0 and P(\(\frac{B}{A}\)) = 1, then
(a) B ⊂ A
(b) B = φ
(c) A ⊂ B
(d) A ∩ B = φ

Answer

Answer: (c) A ⊂ B

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Question 9.
If A and B are any two events such that P(a) + P(b) – P(A∩B) = P(a) then
(a) P(\(\frac{B}{A}\)) = 1
(b) P(\(\frac{B}{A}\)) = 0
(c) P(\(\frac{A}{B}\)) = 1
(d) P(\(\frac{A}{B}\)) = 0

Answer

Answer: (c) P(\(\frac{A}{B}\)) = 1

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Question 10.
If A and B are events such that P (A∪B) = \(\frac{3}{4}\). P(A∩B) = \(\frac{1}{4}\), P(a) = \(\frac{2}{3}\) then P(AB) is
(a) \(\frac{3}{8}\)
(b) \(\frac{5}{8}\)
(c) \(\frac{5}{12}\)
(d) \(\frac{1}{4}\)

Answer

Answer: (b) \(\frac{5}{8}\)

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Question 11.
If one card is drawn out of 52 playing cards, the probability that it is an dice is
(a) \(\frac{1}{26}\)
(b) \(\frac{1}{13}\)
(c) \(\frac{1}{52}\)
(d) \(\frac{1}{4}\)

Answer

Answer: (b) \(\frac{1}{13}\)

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Question 12.
The chance of getting a doublet with 2 dice is
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{6}\)
(c) \(\frac{5}{6}\)
(d) \(\frac{5}{36}\)

Answer

Answer: (b) \(\frac{1}{6}\)

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Question 13.
Two number are chosen, one by one without replacement from the set of number A = {1, 2, 3, 4, 5, 6} then the probability that minimum value of two number chosen is less than 4 is
(a) \(\frac{14}{15}\)
(b) \(\frac{1}{15}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{8}{5}\)

Answer

Answer: (b) \(\frac{1}{15}\)

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Question 14.
If P(x) = \(\frac{2}{15}\); y = 1, 2, 3, 4, 5, 0 otherwise then P|x = 1 or 2| is
(a) \(\frac{1}{15}\)
(b) \(\frac{2}{15}\)
(c) \(\frac{1}{5}\)
(d) None of these

Answer

Answer: (c) \(\frac{1}{5}\)

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Question 15.
Five horse are in a race. Mr. A select two of the horses at random and best on them. The probability that Mr. A select the winning horses is
(a) \(\frac{4}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{2}{5}\)

Answer

Answer: (d) \(\frac{2}{5}\)

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Question 16.
The probability of India w inning a test match against. West Indies is \(\frac{1}{2}\). Assuming independence from match to match the probability that in a match series India second win occurs at the third test is
(a) \(\frac{1}{6}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{2}{3}\)

Answer

Answer: (b) \(\frac{1}{4}\)

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Question 17.
Three distinct numbers.are selected from First 100 natural numbers. The probability divisible by 2 and 3 is
(a) \(\frac{9}{25}\)
(b) \(\frac{4}{35}\)
(c) \(\frac{4}{55}\)
(d) \(\frac{4}{1155}\)

Answer

Answer: (d) \(\frac{4}{1155}\)

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Question 18.
The probability that A speaks truth is \(\frac{4}{5}\) while this probability for B is \(\frac{3}{4}\). The probability that they contradict each others when asked to speak ana fact is
(a) \(\frac{7}{20}\)
(b) \(\frac{1}{5}\)
(c) \(\frac{3}{20}\)
(d) \(\frac{4}{5}\)

Answer

Answer: (d) \(\frac{4}{5}\)

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Question 19.
Two dice are tossed once. The probability of getting an even number at the first dice ora total of 8 is
(a) \(\frac{1}{36}\)
(b) \(\frac{3}{36}\)
(c) \(\frac{11}{36}\)
(d) \(\frac{5}{9}\)

Answer

Answer: (d) \(\frac{5}{9}\)

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Question 20.
The mean and the variance of binomial distribution are 4 and 2, respectively. Then the probability of 2 success
(a) \(\frac{128}{256}\)
(b) \(\frac{219}{256}\)
(c) \(\frac{7}{64}\)
(d) \(\frac{28}{256}\)

Answer

Answer: (c) \(\frac{7}{64}\)

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Question 21.
A pair of dice are rolled. The probability of obtaining an even prime number on each dice is
(a) \(\frac{1}{36}\)
(b) \(\frac{1}{12}\)
(c) \(\frac{1}{6}\)
(d) 0

Answer

Answer: (a) \(\frac{1}{36}\)

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Question 22.
If A, B are two events associated with same random experiment such that P(a) = 0.4, P(b) = 0.8 and P(B/A) = 0.6 then P(A/B) is
(a) 0.3
(b) 0.4
(c) 0.5
(d) 0.6

Answer

Answer: (a) 0.3

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Question 23.
If P(a) = \(\frac{3}{8}\), P(b) = \(\frac{5}{8}\), P(A∪B) = \(\frac{3}{4}\) then p(\(\frac{B}{A}\)) is
(a) \(\frac{3}{47}\)
(b) \(\frac{5}{49}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{4}\)

Answer

Answer: (c) \(\frac{2}{3}\)

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Question 24.
An urn contain’s balls of which 3 are red, 4 are blue and 2 are green, 3 balls are drawn at random without replacement from the urn. The probability that the 3 balls haye different colours is
(a) \(\frac{1}{3}\)
(b) \(\frac{2}{7}\)
(c) \(\frac{1}{21}\)
(d) \(\frac{2}{23}\)

Answer

Answer: (b) \(\frac{2}{7}\)

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Question 25.
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. A consists 4 outcomes, the number of outcomes that B must have so that A and B are independent is
(a) 2, 4 or 8
(b) 36 or 9
(c) 4 or 8
(d) 5 or 10

Answer

Answer: (d) 5 or 10

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Question 28.
If P(a) = \(\frac{4}{5}\) and P(A∩B) = \(\frac{7}{10}\), then P(B/A) is equal
(a) \(\frac{1}{10}\)
(b) \(\frac{1}{8}\)
(c) \(\frac{7}{8}\)
(d) \(\frac{17}{20}\)

Answer

Answer: (d) \(\frac{17}{20}\)

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Question 29.
If P(A∩B) = \(\frac{7}{10}\) and P(b) = \(\frac{17}{20}\), then P(A|B) equals
(a) \(\frac{14}{17}\)
(b) \(\frac{17}{20}\)
(c) \(\frac{7}{8}\)
(d) \(\frac{1}{8}\)

Answer

Answer: (a) \(\frac{14}{17}\)

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Question 30.
If P(a) = \(\frac{7}{10}\) P(b) = \(\frac{7}{10}\) and P(A∪B) = \(\frac{7}{10}\) then P (B|A) + P(A|B) equals
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{5}{12}\)
(d) \(\frac{7}{12}\)

Answer

Answer: (d) \(\frac{7}{12}\)

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Question 31.
If P(a) = \(\frac{2}{5}\), P(b) = \(\frac{3}{10}\) and P (A∩B) = \(\frac{1}{5}\), then P (A’|B’). P(B’|A’) is equal to
(a) \(\frac{5}{6}\)
(b) \(\frac{5}{7}\)
(c) \(\frac{25}{42}\)
(d) 1

Answer

Answer: (c) \(\frac{25}{42}\)

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Question 32.
If P(a) = 0,4, P(b) = 0.8 and P(B|A) = 0.6 then P(A∪B) is equal to
(a) 0.24
(b) 0.3
(c) 0.48
(d) 0.96

Answer

Answer: (d) 0.96

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Question 33.
If A and B are two events and A ≠ Φ, B ≠ Φ, then
(a) P (A|B) = P (a). P (b)
(b) P (A|B) = \(\frac{P(A∩B)}{P(B)}\)
(c) P (A + B). P (B|A) = 1
(d) P (A|B) = P (a) | P (b)

Answer

Answer: (b) P (A|B) = \(\frac{P(A∩B)}{P(B)}\)

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Question 34.
A and B are events such that P(a) = 0.4, P(b) = 0.3 and P(A∪B) = 0.5. Then P(B∩A) equals
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{3}{10}\)
(d) \(\frac{1}{5}\)

Answer

Answer: (d) \(\frac{1}{5}\)

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Question 35.
You are given that A and B are two events such that P(b) = \(\frac{3}{5}\), P(A|B) = \(\frac{1}{2}\) and P (A∪B) = \(\frac{4}{5}\), then P(a) equals
(a) \(\frac{3}{10}\)
(b) \(\frac{1}{5}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)

Answer

Answer: (c) \(\frac{1}{2}\)

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Question 36.
You are given that A and B are two events such that P(b) = \(\frac{3}{5}\), P(A|B) = \(\frac{1}{2}\) and P (A∪B) = then P(B|A’) equals
(a) \(\frac{1}{5}\)
(b) \(\frac{3}{10}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)

Answer

Answer: (d) \(\frac{3}{5}\)

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Question 37.
If P(b) = \(\frac{1}{5}\), P(A|B) = \(\frac{1}{2}\) and P(A∪B) = \(\frac{4}{5}\) then P (A∪B)’ + P (A’∪B) =
(a) \(\frac{1}{5}\)
(b) \(\frac{4}{5}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)

Answer

Answer: (d) \(\frac{3}{5}\)

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Question 38.
Let P (a) = \(\frac{7}{13}\), P(b) = \(\frac{9}{13}\) and P (A∪B) = \(\frac{9}{13}\), Then P(A’|B) is equal to
(a) \(\frac{6}{13}\)
(b) \(\frac{4}{13}\)
(c) \(\frac{4}{9}\)
(d) \(\frac{5}{9}\)

Answer

Answer: (d) \(\frac{5}{9}\)

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Question 39.
If A and B are such that events that P(a) > 0 and P(b) ≠ 1, then P (A’|B’) equal
(a) 1 – P (A|B)
(b) 1 – P(A’|B)
(c) \(\frac{1-P(A∪B)}{P(B’)}\)
(d) p(A’) | P(B’)

Answer

Answer: (c) \(\frac{1-P(A∪B)}{P(B’)}\)

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Question 40.
If two events are independent, then
(a) they must be mutually exclusive
(b) the sum of their probabilities must be equal to 1
(c) (a) and (b) both are correct
(d) None of the above is correct

Answer

Answer: (d) None of the above is correct

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Question 41.
If A and B are two independent events with P(a) = \(\frac{3}{5}\) and P (b) = \(\frac{4}{9}\), then P (A’∩B’) equals
(a) \(\frac{4}{15}\)
(b) \(\frac{8}{15}\)
(c) \(\frac{1}{3}\)
(d) \(\frac{2}{9}\)

Answer

Answer: (d) \(\frac{2}{9}\)

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Question 42.
Let A and B two event such that P(a) = \(\frac{3}{8}\), P(b) = \(\frac{5}{8}\) and P(A∪B) = \(\frac{3}{4}\). Then P(A|B).P(A’|B) is equal to
(a) \(\frac{2}{5}\)
(b) \(\frac{3}{8}\)
(c) \(\frac{3}{20}\)
(d) \(\frac{6}{25}\)
Ans. (d)

Answer

Answer: (d) \(\frac{6}{25}\)

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Question 43.
If the event A and B are independent, then P(A∩B) is equal to
(a) P(a) + P(b)
(b) P(a) – P(b)
(c) P(a). P(b)
(d) P(a) | P(b)

Answer

Answer: (c) P(a). P(b)

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