SUBJECT: ENGINEERING MATHEMATICS IV (MAT 2206] Date of Exam: 10/02/2018 Time of
ID: 3044233 • Letter: S
Question
SUBJECT: ENGINEERING MATHEMATICS IV (MAT 2206] Date of Exam: 10/02/2018 Time of Exam: 9:15 AM-10:15 AM Max. Marks: 15 Instructions to Candidates: Answer ALL the questions If two fair coins are independently tossed 3 times each, the probability that the number of heads obtained on the first coin is equal to the number of heads obtained on the second coin is- ! If A and B are independent events such that P(A)-½ and P(AUB)-X, then ,then1 If a fair die is rolled 3 times, the probability that no two consecutive outcomes are equal is A random variable X has values 1, 2, and 3, with P(X-3)-2P(X-2)-3P(x-). 1 Then P(X 2) Two real numbers are selected from the interval (0,1) at random. Find the probability that they 1 are equal. A box contains 3 defective and 6 other at random (without replacement) and are tested until all the defective balls are detected. What is the probability that the last defective ball is detected at the 7th test? Consider families of n children and let A be the event that a family has children of both the sexes,2 and B the event that there is at most one boy in the family. Find the value of n for which A and B are independent (assuming P(Boy) = P(Girl) = ). fective balls. Balls are selected from the box one after the 2 8. In a college entrance examination, each candidate is admitted or rejected according to whether s/he 2 has passed or failed the entrance test. Of the candidates who are really capable, 80% pass the test; and of the incapable, 25% pass the test. Given that 40% of the candidates are really capable, find the proportion of capable college students? Suppose that X is uniformly distributed over (-a, a) where a>0. Whenever possible, determine a so that the following are satisfied. 10 The random variables X and Y have the ioint distribution civen by the odfExplanation / Answer
#8.
P(really capable) = 0.4
P(pass|really capable) = 0.8
P(incapable) = 0.6
P(pass|incapable) = 0.25
P(capable) = 0.4*0.8 + 0.6*0.25 = 0.47
Hence 47% of students are capable.
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