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## Thursday, 28 January 2021

### CBSE Class 12 Maths - MCQ and Online Tests - Unit 13 - Probability

#### CBSE Class 12 Maths – MCQ and Online Tests – Unit 13 – Probability

Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.

#### CBSE Class 12 Maths – MCQ and Online Tests – Unit 13 – Probability

Question 1.
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: (b) $$\frac{1}{3}$$

Question 2.
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

Question 3.
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: (c) P($$\frac{A}{B}$$) = 1

Question 4.
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: (b) $$\frac{5}{8}$$

Question 5.
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: (b) $$\frac{1}{13}$$

Question 6.
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: (b) $$\frac{1}{6}$$

Question 7.
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: (b) $$\frac{1}{15}$$

Question 8.
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: (c) $$\frac{1}{5}$$

Question 9.
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

Question 10.
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: (d) $$\frac{2}{5}$$

Question 11.
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: (a) P(A∩B) = P(a) × P(b)

Question 12.
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: (b) $$\frac{1}{4}$$

Question 13.
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: (d) $$\frac{5}{6}$$

Question 14.
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: (d) $$\frac{4}{1155}$$

Question 15.
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: (a) $$\frac{1}{36}$$

Question 16.
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: (a) $$\frac{13}{24}$$

Question 17.
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: (d) $$\frac{4}{5}$$

Question 18.
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: (d) $$\frac{7}{12}$$

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

Question 20.
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: (a) $$\frac{1}{36}$$

Question 21.
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

Question 22.
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: (c) $$\frac{2}{3}$$

Question 23.
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: (b) P($$\frac{B}{A}$$) = 1

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

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

Question 26.
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: (c) $$\frac{7}{64}$$

Question 27.
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: (d) $$\frac{17}{20}$$

Question 28.
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: (a) $$\frac{14}{17}$$

Question 29.
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: (d) $$\frac{2}{9}$$

Question 30.
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: (d) $$\frac{6}{25}$$

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