NCERT Solutions for Class 12 Maths<\/a> Chapter 13 Probability Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-13-miscellaneous-exercise\/<\/p>\nNCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercise<\/h2>\n <\/p>\n
Question 1. \nA and B are two events such that P (A) \u2260 0. Find P(B|A), if \ni. A is a subset of B \nii. A \u2229 B = \u03a6 \nSolution: \n <\/p>\n
Question 2. \nA couple has two children. \nFind the probability that both children are males, if it is known that atleast one of the children is male. \nSolution: \nThe sample space, S = {MM, MF, FM, FF}, \nwhere M denote male and F denote female. \nLet A: both children are males \nB : atleast one child is a male \nA = {MM}, \nB = {MM, MF, FM} \n\\(\\mathrm{A} \\cap \\mathrm{B}=\\{\\mathrm{MM}\\}, \\mathrm{P}(\\mathrm{A})=\\frac{1}{4}\\) \n\\(P(B)=\\frac{3}{4}, P(A \\cap B)=\\frac{1}{4}\\)<\/p>\n
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Question 3. \nIf a leap year is selected at random, what is the chance that it will contain 53 Tuesdays? \nSolution: \nA leap year contains 366 days = 52 weeks + 2 days \nThe last 2 days can be \ni. Monday, Tuesday \nii. Tuesday, Wednesday \niii. Wednesday, Thursday \niv. Thursday, Friday \nv. Friday, Saturday \nvi. Saturday, Sunday \nvii. Sunday, Monday \nOf these seven possibilities, (i) & (ii) are favourable to 53 Tuesdays. \n\u2234 P(53 Tuesday) = \\(\\frac { 2 }{ 7 }\\)<\/p>\n
Question 4. \nAn experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes. \nSolution: \nLet p be the probability of a success and q the probability of failure. \nThen p + q – 1 and p = 2q \nSolving p = \\(\\frac { 2 }{ 3 }\\) and q = \\(\\frac { 1 }{ 3 }\\) \nLet X be the number of success. \nThen X is a binomial distribution with \n <\/p>\n
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Question 5. \nHow many times must a man toss a fair coin so that the probability of having atleast one head is more than 90%? \nSolution: \nTossing a coin many times is a Bernoulli trial. Here success is obtaining a Head. \n\u2234 P = \\(\\frac { 1 }{ 2 }\\) \nq = 1 – p = 1 – \\(\\frac { 1 }{ 2 }\\) = \\(\\frac { 1 }{ 2 }\\) \nLet X be the number of heads obtained \nThen X is a binomial distribution B(n, \\(\\frac { 1 }{ 2 }\\)) \n \nWe know 21<\/sup> = 2, 2\u00b2 = 4, 2\u00b3 = 8, 24<\/sup> = 16, 25<\/sup> = 32 and so on \nHence the minimum value of n is 4 i.e. n > 4 \ni.e. the man has to toss the coin atleast 4 times.<\/p>\nQuestion 6. \nIn a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six, Find the expected value of the amount he wins\/loses. \nSolution: \nThe game ends in the following ways. \ni. The man gets 6 in 1st<\/sup> throw. In this case, he earns \u20b9 1. \nP(getting 6 \u00a1n 1st<\/sup> throw) = \\(\\frac { 1 }{ 6 }\\)<\/p>\nii. The man does not get 6 in 1nd<\/sup> throw and 6 in 2nd<\/sup> throw. In this case he earns \u20b9 0 \n(In 1st<\/sup> throw, he earns \u20b9 1 and in 2nd<\/sup> throw he loses \u20b9 1) \nP(not getting 6 on 1st<\/sup> throw & 6 in 2nd<\/sup> throw) = (\\(\\frac { 5 }{ 6 }\\))(\\(\\frac { 1 }{ 6 }\\)) = \\(\\frac { 5 }{ 6 }\\)<\/p>\n <\/p>\n
Question 7. \nSuppose we have four boxes A, B, C and D containing coloured marbles as given below: \n \nOne of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A? box B? \nSolution: \nLet E1<\/sub> : selecting box A \nE2<\/sub> : selecting box B \nE3<\/sub> : selecting box C \nE4<\/sub> : selecting box D \nA : selecting a red ball \nE1<\/sub>, E2<\/sub>, E3<\/sub> and E4<\/sub> are mutually exclusive and exhaustive events. \n\u2234 \\(\\mathrm{P}\\left(\\mathrm{E}_{1}\\right)=\\mathrm{P}\\left(\\mathrm{E}_{2}\\right)=\\mathrm{P}\\left(\\mathrm{E}_{3}\\right) \\dot{\\mathrm{P}}\\left(\\mathrm{E}_{4}\\right)=\\frac{1}{4}\\) \n\\(\\mathrm{P}\\left(\\mathrm{A} \\mid \\mathrm{E}_{1}\\right)=\\frac{1}{10}, \\quad \\mathrm{P}\\left(\\mathrm{A} \\mid \\mathrm{E}_{2}\\right)=\\frac{6}{10}\\)<\/p>\nQuestion 8. \nBag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black. \nSolution: \nE1<\/sub> : a red ball is transferred from bag I to bag II \nE2<\/sub> : a black ball is transferred from bag I to bag II \nA : a red ball is taken from bag II after transferring a ball \nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive events \n <\/p>\nQuestion 9. \nIf A B are two events such that P(A) \u2260 0 and P(B|A) = 1, then \na. A \u2229 B \nb. B \u2229 A \nc. B = \u03a6 \nd. A = \u03a6 \nSolution: \n <\/p>\n
Question 10. \nIf P(A|B) > P(A), then which of the following is correct: \na. P(B | A) < P(B) \nb. P(A \u2229 B) < P(A). P(B) c. P(B | A) > P(B) \nd. P(B | A) = P(B) \nSolution: \n <\/p>\n
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Question 11. \nIf A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then \na. P(B|A) = 1 \nb. P(A|B) = 1 \nc. P(B|A) = 0 \nd. P(A|B) = 0 \nSolution: \n <\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-13-miscellaneous-exercise\/ NCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercise Question 1. A and B are two events such that P (A) \u2260 0. Find P(B|A), if i. A is …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercise<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercise - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n