{"id":19310,"date":"2021-02-27T11:12:34","date_gmt":"2021-02-27T05:42:34","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=19310"},"modified":"2021-02-27T11:12:34","modified_gmt":"2021-02-27T05:42:34","slug":"mcq-questions-for-class-12-maths-chapter-13","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/mcq-questions-for-class-12-maths-chapter-13\/","title":{"rendered":"MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Probability Class 12 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 12 Maths Chapter 13 Probability Objective Questions.<\/p>\n

Probability Class 12 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Probability Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Probability Class 12 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Probability Class 12 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nIf P(A) = \\(\\frac { 1 }{2}\\), P(B) = 0, thenP (A\/B) is
\n(a) 0
\n(b) \\(\\frac { 1 }{2}\\)
\n(c) not defined
\n(d) 1.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) not defined<\/p>\n<\/details>\n

\n

Question 2.
\nIf A and B are events such that P (A\/B) = P(B\/A), then
\n(a) A \u2282 B but A \u2260 B
\n(b) A = B
\n(c) A \u2229 B = \u00f8
\n(d) P (A) = P (B).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) P (A) = P (B).<\/p>\n<\/details>\n

\n

Question 3.
\nThe probability of obtaining an even prime number on each die when a pair of dice is rolled is
\n(a) 0
\n(b) \\(\\frac { 1 }{3}\\)
\n(c) \\(\\frac { 1 }{12}\\)
\n(d) \\(\\frac { 1 }{36}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac { 1 }{36}\\)<\/p>\n<\/details>\n

\n

Question 4.
\nTwo events A and B are said to be independent if:
\n(a) A and B are mutually exclusive
\n(b) P (A’B’) = [1 – P(A)] [1 – P(B)]
\n(c) P (A) = P (B)
\n(d) P (A) + P (B) = 1.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) P (A’B’) = [1 – P(A)] [1 – P(B)]<\/p>\n<\/details>\n

\n

Question 5.
\nProbability that A speaks truth is \\(\\frac { 4 }{5}\\). A coin is tossed. A reports that a head appears. The probability that actually there was head is:
\n(a) \\(\\frac { 4 }{5}\\)
\n(b) \\(\\frac { 1 }{2}\\)
\n(c) \\(\\frac { 1 }{5}\\)
\n(d) \\(\\frac { 2 }{5}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) \\(\\frac { 4 }{5}\\)<\/p>\n<\/details>\n

\n

Question 6.
\nIf A and B are two events such that A \u2282 B and P (B) \u2260 0, then which of the following is correct
\n(a) P (A \/ B) = \\(\\frac { p(B) }{p(A)}\\)
\n(b) P (A\/B) < P (A)
\n(c) P (A\/B) \u2265 P (A)
\n(d) None of these.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) P (A\/B) \u2265 P (A)<\/p>\n<\/details>\n

\n

Question 7.
\nIf A and B are two events such that P (A) \u2260 0 and P (B\/A) = 1, then
\n(a) A \u2282 B
\n(b) B \u2282 A
\n(c) B = \u00f8
\n(d) A = \u00f8<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) A \u2282 B<\/p>\n<\/details>\n

\n

Question 8.
\nIf P (A\/B) > P (A), then which of the following is correct?
\n(a) P (B\/A) < P (B)
\n(b) P (A \u2229 B) < P (A).P(B)
\n(c) P (B\/A) > P (B)
\n(d) P (B\/A) = P (B).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) P (B\/A) > P (B)<\/p>\n<\/details>\n

\n

Question 9.
\nIf A and B are any two events such that
\nP (A) + P (B) – P (A and B) = P (A), then:
\n(a) P (B\/A) = 1
\n(b) P (A\/B) = 1
\n(c) P (B\/A) = 0
\n(d) P (A\/B) = 0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) P (A\/B) = 1<\/p>\n<\/details>\n

\n

Question 10.
\nSuppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. What is the value of E (X)?
\n(a) \\(\\frac { 37 }{221}\\)
\n(b) \\(\\frac { 5 }{13}\\)
\n(c) \\(\\frac { 1 }{13}\\)
\n(d) \\(\\frac { 2 }{13}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac { 2 }{13}\\)<\/p>\n<\/details>\n

\n

Question 11.
\nA die is thrown once, then the probability of getting a number greater than 3 is :
\n(a) \\(\\frac { 1 }{2}\\)
\n(b) \\(\\frac { 2 }{3}\\)
\n(c) 6
\n(d) 0.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) \\(\\frac { 1 }{2}\\)<\/p>\n<\/details>\n

\n

Question 12.
\nLet A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A \u222a B) = 0.6, then P(A\/B) is equal to:
\n(a) 0.8
\n(b) 0.5
\n(c) 0.3
\n(d) 0.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 0.<\/p>\n<\/details>\n

\n

Question 13.
\nLet A and B be two events such that P(A) = 0.6, P(B) = 0.2 and P(A\/B) = 0.5. Then P(A’\/B’) equals
\n(a) \\(\\frac { 1 }{10}\\)
\n(b) \\(\\frac { 3 }{10}\\)
\n(c) \\(\\frac { 3 }{8}\\)
\n(d) \\(\\frac { 6 }{7}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { 3 }{8}\\)<\/p>\n<\/details>\n

\n

Question 14.
\nIf A and B are independent events such that 0 < P(A) < 1 and 0 < P(B) < 1, then which of the following is not correct?
\n(a) A and B are mutually exclusive
\n(b) A and B’ are independent
\n(c) A’ and B are independent
\n(d) A’ and B’ are independent.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) A and B are mutually exclusive<\/p>\n<\/details>\n

\n

Question 15.
\nLet \u2018X\u2019 be a discrete random variable. The probability distribution of X is given below
\n\"MCQ
\nThen E(X) is equal to
\n(a) 6
\n(b) 4
\n(c) 3
\n(d) (-5).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 4<\/p>\n<\/details>\n

\n

Question 16.
\nLet \u2018X\u2019 be a discrete random variable assuming values x1<\/sub>, x2<\/sub>, …………… , xn<\/sub> with probabilities p1<\/sub>, p2<\/sub>, …………. , pn<\/sub> respectively. Then variance of \u2018X\u2019 is given by
\n(a) E(X\u00b2)
\n(b) E(X\u00b2) + E(X)
\n(c) E(X\u00b2) – [E(X)]\u00b2
\n(d) \\(\\sqrt { E(X)^2-[E(X)]^2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) E(X\u00b2) – [E(X)]\u00b2<\/p>\n<\/details>\n

\n

Question 17.
\nIf it is given that the events A and B are such that P (A) = \\(\\frac { 1 }{4}\\), P (A\/B) = \\(\\frac { 1 }{2}\\) and P(B\/A) = \\(\\frac { 2 }{3}\\). Then P (B) is:
\n(a) \\(\\frac { 1 }{2}\\)
\n(b) \\(\\frac { 1 }{6}\\)
\n(c) \\(\\frac { 1 }{3}\\)
\n(d) \\(\\frac { 2 }{3}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { 1 }{3}\\)
\nHint:
\nBy definition, P (A\/B) = \\(\\frac { P(A\u2229B) }{P(B)}\\)
\n\u21d2 P(B) P(A\/B) = P(A\u2229B) ……….(1)
\nSimilarly P(A) P(B\/A) = P(B\u2229A) ……….(2)
\nFrom (1) and (2), P(A) P(B\/A)
\n= P(B) P(A\/B)
\n[\u2235 P(A\u2229B) = PP(B\u2229A)]
\n\u21d2 \\(\\frac { 1 }{4}\\).\\(\\frac { 2}{3}\\) = P(B).\\(\\frac { 1 }{2}\\)
\n\u21d2 P(B) = \\(\\frac { 1 }{4}\\).\\(\\frac { 2 }{3}\\).2 = \\(\\frac { 1 }{3}\\)<\/p>\n<\/details>\n

\n

Question 18.
\nIf A and B are two events such that P(A) = 0.2, P(B) = 0.4 and P(A\u222aB) = 0.5, then value of P(A\/B) is?
\n(a) 0.1
\n(b) 0.25
\n(c) 0.5
\n(d) 0.08.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 0.25
\nHint:
\nP(A\u222aB) = P(A) + P(B) – P(A\u2229B)
\n\u21d2 0.5 = 0.2 + 0.4 – P(A\u2229B)
\n\u21d2 P(A\u2229B) = 0.6 – 0.5 = 0.1.
\n\u2234 P(A\u2229B) = \\(\\frac { P(A\u2229B) }{P(B)}\\) = \\(\\frac { 0.1 }{0.4}\\) = 0.25<\/p>\n<\/details>\n

\n

Question 19.
\nAn urn contains 6 balls of which two are red and four are black. Two balls are drawn at random. Probability that they are of the different colours is:
\n(a) \\(\\frac { 2 }{5}\\)
\n(b) \\(\\frac { 1 }{15}\\)
\n(c) \\(\\frac { 8 }{15}\\)
\n(d) \\(\\frac { 4 }{15}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { 8 }{15}\\)
\nHint:
\nReqd. probability = P(RB) + P (BR)
\n(R \u2261 Red ball and B \u2261 Black ball)
\n= (\\(\\frac { 2 }{6}\\) \u00d7 \\(\\frac { 4 }{5}\\)) + (\\(\\frac { 4 }{6}\\) \u00d7 \\(\\frac { 2 }{5}\\)) = \\(\\frac { 4 }{15}\\) + \\(\\frac { 4 }{15}\\) = \\(\\frac { 8 }{15}\\)<\/p>\n<\/details>\n

\n

Question 20
\nLet A, B, C be pairwise independent events with P (C) > 0 and P (A\u2229B\u2229C) = 0. Then P (Ac<\/sup>\u2229Bc<\/sup> \/C) is
\n(a) P (A) – P (Bc<\/sup>)
\n(b) P (Ac<\/sup>) + P (Bc<\/sup>)
\n(c) P (Ac<\/sup>) – P (Bc<\/sup>)
\n(d) P (Ac<\/sup>) – P (B).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) P (Ac<\/sup>) – P (B).
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 21.
\nThree numbers are chosen at random with-out replacement from {1, 2, 3, ….. 8}. The probability that their minimum is 3, given that their maximum is 6 is
\n(a) \\(\\frac { 3 }{8}\\)
\n(b) \\(\\frac { 1 }{5}\\)
\n(c) \\(\\frac { 1 }{4}\\)
\n(d) \\(\\frac { 2 }{5}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\frac { 1 }{5}\\)
\nLet the events be ({1, 2, 3, ….. , 8})
\nA : Maximum of three numbers is 6
\nB : Minimum of three numbers is 3.
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 22.
\nLet A and B be two events such that P\\((\\overline{\\mathbf{A} \\cup \\mathbf{B}})\\) = \\(\\frac { 1 }{6}\\) P(A\u2229B) = \\(\\frac { 1 }{4}\\) and P(\\(\\bar { A}\\)) = \\(\\frac { 1 }{4}\\), where \\(\\bar { A}\\)stands for the complement of the event A. Then the events A and B are
\n(a) equally likely but not independent
\n(b) independent but not equally likely
\n(c) independent and equally likely
\n(d) mutually exclusive and independent.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) independent but not equally likely
\nP\\((\\overline{\\mathbf{A} \\cup \\mathbf{B}})\\) = \\(\\frac { 1 }{6}\\), P(A\u222aB) = \\(\\frac { 5 }{6}\\), P(A) = \\(\\frac { 3 }{4}\\).
\nNow P(A\u222aB) = P(A) + P(B) – P(A\u2229B)
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 23.
\nIf two different numbers are taken from set (0, 1, 2, …… , 10}, then the probability that their sum as well as absolute difference are both multiples of 4, is
\n(a) \\(\\frac { 14 }{45}\\)
\n(b) \\(\\frac { 7 }{55}\\)
\n(c) \\(\\frac { 6 }{55}\\)
\n(d) \\(\\frac { 12 }{55}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { 6 }{55}\\)
\nHint:
\nLet A = {0, 1, 2, 3, …….. , 10}
\n\u2234 n(S) = 11<\/sup>C2<\/sub> = 55.
\nLet E be the given event.
\n\u2234 E = {(0, 4), (0, 8), (2, 6), (2, 10), (4, 8), (6, 10) }.
\n\u2234n(E) = 6
\nHence P(E) = \\(\\frac { n(E) }{n(S)}\\) = \\(\\frac { 6 }{55}\\)<\/p>\n<\/details>\n

\n

Question 24.
\nA bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag.
\nIf now a ball is drawn at random from the bag, then the probability that this drawn ball is red is
\n(a) \\(\\frac { 3 }{10}\\)
\n(b) \\(\\frac { 2 }{5}\\)
\n(c) \\(\\frac { 1 }{5}\\)
\n(d) \\(\\frac { 3 }{4}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\frac { 2 }{5}\\)
\nHint:
\nLet E1<\/sub> : Event that first ball is red
\nE2<\/sub> : Event that first ball is black and
\nE3<\/sub> : Event that second is the red.
\nNow, P(E) = P(E1<\/sub>) P |E\/E1<\/sub>| + P (E2<\/sub>)P(E\/E2<\/sub>)
\n= \\(\\frac { 4 }{10}\\) \u00d7 \\(\\frac { 6 }{12}\\) + \\(\\frac { 6 }{10}\\) \u00d7 \\(\\frac { 4 }{12}\\)
\n= \\(\\frac { 1 }{5}\\) + \\(\\frac { 1 }{5}\\) = \\(\\frac { 2 }{5}\\)<\/p>\n<\/details>\n

\n

Fill in the blanks<\/span><\/p>\n

Question 1.
\nIf P(A) = \\(\\frac { 1 }{5}\\) and P(A – B) = \\(\\frac { 1 }{6}\\), then P(A\u2229B) = ………………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{30}\\)<\/p>\n<\/details>\n

\n

Question 2.
\nThe probability of \u2018Ace of spade\u2019 is ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{52}\\)<\/p>\n<\/details>\n

\n

Question 3.
\nIf P(A) = \\(\\frac { 6 }{11}\\), P(B) = \\(\\frac { 5 }{11}\\) and P(A\u222aB) = then P(B\/A) = ……………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 6 }{11}\\)<\/p>\n<\/details>\n

\n

Question 4.
\nIf A and B are independent events, then P(A\u2229B) = ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: P(A) P(B).<\/p>\n<\/details>\n

\n

Question 5.
\nIf P(\\(\\bar { A}\\)) = 0.4, P(A\u222aB) = 0.7 and A and B are given to be independent events, then P(B) = ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{4}\\)<\/p>\n<\/details>\n

\n

Question 6.
\nIf A and B are two independent events such that P(A) = \\(\\frac { 1 }{2}\\), P(A\u222aB) = \\(\\frac { 3 }{5}\\) and P(A) = p, then p = ………………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{5}\\)<\/p>\n<\/details>\n

\n

Question 7.
\nIf A and B are independent events such that P(A) = \\(\\frac { 3 }{10}\\), P(B) = \\(\\frac { 2 }{5}\\) then P(A and B) is ……………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 3 }{25}\\)<\/p>\n<\/details>\n

\n

Question 8.
\nA pair of coins is tossed once. Then the probability of showing at least one head is ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 3 }{4}\\)<\/p>\n<\/details>\n

\n

Question 9.
\nA random variable \u2018X\u2019 has a probability distribution P(X) of the following form (k is constant)
\n\"MCQ
\nThen k is ……………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{6}\\)<\/p>\n<\/details>\n

\n

Question 10.
\nThe mean of the number of heads in the two tosses of a coin is …………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 1.<\/p>\n<\/details>\n

\n

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Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students can download …<\/p>\n

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