14%20-%20Probability

14%20-%20Probability - 14 - PROBABILITY Page 1 ( Answers at...

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14 - PROBABILITY Page 1 ( Answers at the end of all questions ) ( 1 ) Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is ( a ) 9 2 ( b ) 9 1 ( c ) 9 8 ( d ) 9 7 [ AIEEE 2005 ] ( 2 ) A random variable X has Poisson distribution with mean 2. Then P ( x > 1.5 ) equals ( a ) 2 e 2 ( b ) 0 ( c ) 1 - 2 e 3 ( d ) 2 e 3 [ AIEEE 2005 ] ( 3 ) Let A and B be two events such that P ( B A ) = 6 1 , P ( B A ) = 4 1 and P ( A ) = 4 1 , where A stands for complement of event A. Then events A and B are ( a ) equally likely and mutually exclusive ( b ) equally likely but not independent ( c ) independent but not equally likely ( d ) mutually exclusive and independent [ AIEEE 2005 ] ( 4 ) Let x 1 , x 2 , …. ., x n be n observations such that 2 i x = 400 and i x = 80. Then a possible value of n among the following is ( a ) 15 ( b ) 18 ( c ) 9 ( d ) 12 [ AIEEE 2005 ] ( 5 ) Probability that A speaks truth is 5 4 while this probability for B is 4 3 . The probability that they contradict each other when asked to speak on a fact is ( a ) 20 3 ( b ) 5 1 ( c ) 20 7 ( d ) 5 4 [ AIEEE 2004 ] ( 6 ) The mean and variance of a random variable x having a binomial distribution are 4 and 2 respectively. Then P ( x = 1 ) is ( a ) 256 37 ( b ) 256 219 ( c ) 256 128 ( d ) 256 28 [ AIEEE 2004 ]
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- PROBABILITY Page 2 ( Answers at the end of all questions ) ( 7 ) A random variable X has the following probability distribution. X : 1 2 3 4 5 6 7 8 p ( X ) : 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 For the events E = { X is a prime number } and F = { X < 4 }, the probability P ( E F ) is ( a ) 0.87 ( b ) 0.77 ( c ) 0.35 ( d ) 0.50 [ AIEEE 2004 ] ( 8 ) The events A, B, C are mutually exclusive events such that P ( A ) = 3 1 x 3 + , P ( B ) = 4 x 1 - and P ( C ) = 2 2x 1 - . The set of possible values of x are in the interval ( a ) 2 1 , 3 1 ( b ) 3 2 , 3 1 ( c ) 3 13 , 3 1 ( d ) [ 0, 1 ] [ AIEEE 2003 ] ( 9 ) Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is ( a ) 5 4 ( b ) 5 3 ( c ) 5 1 ( d ) 5 2 [ AIEEE 2003 ] ( 10 ) The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively. Then, P ( X = 1 ) is ( a ) 32 1 ( b ) 16 1 ( c ) 8 1 ( d ) 4 1 [ AIEEE 2003 ] ( 11 ) The probabilities of a student getting I st, II nd and III rd division in an examination are respectively 10 1 , 5 3 and 4 1 . The probability, that a student fails in the examination is ( a ) 200 197 ( b ) 100 27 ( c ) 100 83 ( d ) 200 33 [ AIEEE 2002 ] ( 12 ) A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. If from the selected bag one ball is drawn, then the probability that the ball drawn is red is
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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14%20-%20Probability - 14 - PROBABILITY Page 1 ( Answers at...

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