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»1, A university has to select an examiner from a list, , 32., , 33., , of 50 persons, 20 of them are women and 30 men, |, 10 of them knowing Hindi and 40 not, 15 of them |, being teachers and the remaining 35 not. What is, the probability of the university selecting a Hindi |, knowing woman teacher?, , 1 2 4 3, @) is (b) i (c) a (d) =, , Let E,, E,, E,, .... E, be independent events with |, respective probabilities p,, p,, Py... Py» Find the ©, probability that (i) none of them occurs (ii) atleast, one of them occurs., , , , , , , , , , , , , , , , , , , , , , (i) (i), (a) | (1-p,)(1-p,)... 1-[(1-p,) (1-p,)..., | [G-p,) Kc), (b) (l-p)Q-p,) 1 [.- p)-p))], © &,-p,) 1-(@,-p,), (d) none ofthese, , , , Given that, the events A and B are such that P(A) = * ?, , P(AUB) == and P(B) = p. Then probabilities of B :, , if A and B are mutually exclusive and independent, , respectively are ;, rile it 2 1 1, cent {hy eae f= (4d) ==, , ) 05 O33 © 33 ws
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35, Probability of solving on problem independently, , 1, by Aand Bare a and ~ 3 respectively. Ifboth try to solve, , the problem iaependenty then the probabilities that, the problem is solved and exactly one of them solve, the problem respectively are, , fae) (ey ee Iles, , ia, =a) | he), 3 3 32 5 3, , Wwlrm, , Z, 2, , Bayes' Theorem, , 36., , 37., , Urn 1 contains 5 white balls and 7 black balls. Urn, 2 contains 3 white and 12 black. A fair coin is flipped,, if it is heads, a ball is drawn from urn 1, and if it is, tails, a ball is drawn from urn 2. Suppose that this, experiment is done and a white ball was selected., What is the probability that this ball was in fact, taken from urn 2? (i.e., that the coin flip was tails), , I>, , @2 oi @o@ 2 os, 37 10 37 24, , Two cards from an ordinary deck of 52 cards are, , missing. What is the probability that a random card, , drawn from this deck is a spade?, , 3 2 Bile i, (a) 4 (b) 3 (c) 3 (d) 4
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38., , 39., , One half percent of the population has a particular, disease. A test is developed for the disease. The test, givesa false positive 3% ofthe time anda false negative, 2% of the time. What is the probability that Amit, (a random person) tests positive?, , (a) 0.476 (b) 0.035 (c) 0.523 (d) 0.232, , The bag 'A' contains 5 white and 3 black balls while, the bag 'B' contains 4 white and 7 black balls. One, of the bags is chosen at random and a ball is drawn, from it. What is the probability that the ball is white?, , , , @ 2 wt ogo 2 we, , 176 172 179 179, One-thirds of the students of a class are boys and, the rest are girls. It is known that the probability of a, girl getting a first class marks in Board's Exam is 0.6, and a boy getting first class marks is 0.35. Find the, , probability that a student chosen at random will get, first class marks in exam., , af 33 31 31, b —— ., (a) 60 (b) =p (c) rs (d) 50
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41., , 42., , 43., , Bag P contains 6 red and 4 blue balls and bag Q ©, contains 5 red and 6 blue balls. A ball is transferred, from bag P to bag Qand then a ball is drawn from bag, Q. What is the probability that the ball drawn is blue?, 8, , @ 2 wo & wo} 4 WwW, , 15 15 19 19, A fair die is rolled. If 1 turns up a ball is picked up at, random from bag P. If2 or 3 turns up, a ball is picked, up from bag Q. If 4, 5 or 6 turns up, a ball is picked up, from bag R. Bag P contains 5 red and 3 white balls;, bag Qcontains 4 red and 3 white balls; bag R contains, 3 red and 6 white balls. The die is rolled, a bag is, picked and a ball is drawn. Find the probability that, a red ball is drawn., , 154 154 155 155, , = i) 2 2 ify =, ) 337 ©) 339 (<) 337 (¢) 336, Coloured balls are distributed in three bags as, shown in the following table :, , , , , , , , ergs] 2 pColontolbell:, , Bag Green ‘Black Blue |, I 1 a 2 | 3., II 2 4 1, III 3 3 2, , A bag is selected at random and then two balls are, drawn from the selected bag. Find the probability, that the balls drawn are black and blue., , 163 161 169 167, , (a) 630 (b) 630 (c) a (d) on
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45. There are two groups of subjects, one of which, consists of 6 Science and 4 Engineering subjects; and, the other consists of 4 Science and 6 Engineering, subjects. An unbiased die is rolled. If number 1 or, 6 turn up, a subject is selected at random from the, first group, otherwise a subject is selected from the, second group. If ultimately an engineering subject is, selected, then find the probability that it is selected, , from second group., , @ 2 ow 2 @ 1 @t, 4 3 2
