{"id":32760,"date":"2021-08-31T17:59:51","date_gmt":"2021-08-31T12:29:51","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=32760"},"modified":"2021-08-31T17:59:51","modified_gmt":"2021-08-31T12:29:51","slug":"ncert-solutions-for-class-12-maths-chapter-13-ex-13-3","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-13-ex-13-3\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 13 Probability Ex 13.3 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.3<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nAn urn contain 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random.What is the probability that the second ball is red?
\nSolution:
\nUrn contain 5 red and 5 black balls.
\n(i) Let a red ball is drawn.
\nprobability of drawing a red ball = \\(\\frac { 5 }{ 10 }\\) = \\(\\frac { 1 }{ 2 }\\)
\nNow two red balls are added to the urn.
\n\u21d2 The urn contains 7 red and 5 black balls.
\nProbability of drawing a red ball = \\(\\frac { 7 }{ 12 }\\)<\/p>\n

(ii) Let a black ball is drawn at first attempt
\nProbability of drawing a black ball = \\(\\frac { 5 }{ 10 }\\) = \\(\\frac { 1 }{ 2 }\\)
\nNext two black balls are added to the urn
\nNow urn contains 5 red and 7 black balls
\nProbability of getting a red ball = \\(\\frac { 5 }{ 12 }\\)
\n\u21d2 Probability of drawing a second ball as red
\n= \\(\\frac { 1 }{ 2 } \\times \\frac { 7 }{ 12 } +\\frac { 1 }{ 2 } \\times \\frac { 5 }{ 12 } =\\frac { 7 }{ 24 } +\\frac { 5 }{ 24 } =\\frac { 12 }{ 24 } =\\frac { 1 }{ 2 }\\)<\/p>\n

Question 2.
\nA bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
\nSolution:
\nE1<\/sub> : first bag is selected
\nE2<\/sub> : second
\nbag is selected A : ball drawn is red
\nE1<\/sub> and E2<\/sub> are mutually exclusive & exhaustive events
\nP(E1<\/sub>) = P(E2<\/sub>) =
\nP(A|E1<\/sub>) = \\(\\frac { 4 }{ 8 }\\) and P(A|E2<\/sub>) = \\(\\frac { 2 }{ 8 }\\)
\nBy Bayes\u2019 theorem
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nOf the students In a college, it is known that 60% reside In hostel and 40% are day scholars (not residing In hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student Is chosen at random from the college and he has an A- grade what Is the probability that the student is a hostlier?
\nSolution:
\nE1<\/sub> : student is a hosteler
\nE2<\/sub> : student is a day scholar
\nA : student attains A grade.
\nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive
\n\"NCERT<\/p>\n

Question 4.
\nIn answering a question on a multiple choice test, a student either knows the answer or 3 guesses. Let \\(\\frac { 3 }{ 4 }\\) be the probability that he knows the answer and \\(\\frac { 1 }{ 4 }\\) be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability \\(\\frac { 1 }{ 4 }\\) . What is the probability that the student knows the answer given that he answered it correctly?
\nSolution:
\nLet E1<\/sub> : student knows the answer
\nE2<\/sub> : student guesses the answer
\nA : student answers correctly
\nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive events.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 5.
\nA laboratory blood test is 99% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
\nSolution:
\nLet E1<\/sub> : the person has a disease
\nE2<\/sub> : the person is healthy
\nA : the test result is positive
\nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive events.
\n\"NCERT<\/p>\n

Question 6.
\nThere are three coins. One is a two headed coin, another is a biased coin that conies up heads 75% of the time and third is an unbiased coin. One of the three coins is choosen at random and tossed, it shows head, what is the probability that it was the two headed coin?
\nSolution:
\nLet
\nE1<\/sub> : coin tossed is two headed
\nE2<\/sub> : coin tossed is biased
\nE3<\/sub> : coin tossed is unbiased
\nA: getting head
\nE1<\/sub> and E2<\/sub> and E3<\/sub> are mutually exclusive and exhaustive events.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 7.
\nAn insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of mi accident are 0.01, 0.03, 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?
\nSolution:
\nLet
\nE1<\/sub> : insured person is a scooter driver
\nE2<\/sub> : insured person is a car driver
\nE3<\/sub> : insured person is a truck driver and
\nA : insured person meets with an accident.
\nE1<\/sub> E2<\/sub> and E3<\/sub> are mutually exclusive and exhaustive events.
\nTotal number of insured person
\n= 2000 + 4000 + 6000 = 12000
\n\"NCERT<\/p>\n

Question 8
\nA factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective.All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B.?
\nSolution:
\nLet
\nE1<\/sub> : item produced by machine A
\nE1<\/sub> : item produced by machine B
\nA : item is defective
\nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive events
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 9.
\nTwo groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.
\nSolution:
\nLet E1<\/sub> : first group wins
\nE2<\/sub> : second group wins
\nA : introducing a new product
\nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive events
\n\"NCERT<\/p>\n

Question 10.
\nSuppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads.If she gets 1,2,3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1,2,3, or 4 with the die?
\nSolution:
\nWhen she gets 5,6, she throws a coin three times.
\nThe events are
\nE1<\/sub> : getting 1, 2, 3, 4
\nE2<\/sub> : getting 5, 6
\nA : getting exactly one head
\nE1<\/sub> and E2<\/sub> are mutually exclusive and exhaustive events
\nP(E1<\/sub>) = \\(\\frac { 4 }{ 6 }\\) P(E2<\/sub>) = \\(\\frac { 2 }{ 6 }\\)
\nWhen she gets 1,2,3,4, .she throws a coin once.
\nP(A|E1<\/sub>) = \\(\\frac { 1 }{ 2 }\\)
\nWhen a coin is tossed 3 times, the sample space is {HHH, HHT,- HTH, HTT, THH, THT, TTH, TTT}
\nOne head is obtained as {HTT, THT, TTH} P(A|E2<\/sub>) = \\(\\frac { 3 }{ 8 }\\)
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 11.
\nA manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?
\nSolution:
\nLet E1<\/sub> : item produced by operator A
\nE2<\/sub> : item produced by operator B
\nE3<\/sub> : item produced by operator C
\nA : event of getting a defective item
\nE1<\/sub>, E2<\/sub> and E3<\/sub> are pairwise disjoint and exhaustive events
\n\"NCERT<\/p>\n

Question 12.
\nA card from a pack of 52 cards is lost From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond?
\nSolution:
\nLet E1<\/sub>: lost card is a diamond
\nE2<\/sub> : lost card is not a diamond
\nA : getting 2 diamond cards from 51 cards
\nE1<\/sub>, E2<\/sub> are mutually exclusive and exhaustive events
\n\"NCERT<\/p>\n

Question 13.
\nProbability that A speaks truth is 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 }\\)
\nSolution:
\nLet E1<\/sub> getting a head
\nE2<\/sub>: getting a tail
\nF : A reports \u2018head occurred\u2019
\nE1<\/sub> and E2<\/sub> are mutually exclusive and ex-haustive events
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 14.
\nIf A and B are two events such that A\u2282B 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
\nSolution:
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.3 Question 1. An urn contain 5 red and 5 black balls. A ball is drawn at random, its colour is noted …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3<\/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":{"spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-13-ex-13-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3 Questions and Answers are prepared by our highly skilled subject experts. 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NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.3 Question 1. An urn contain 5 red and 5 black balls. 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