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

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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 2 3 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 ( 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 ( 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 37 219 128 28 [ AIEEE 2004 ]
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14 - 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 ( 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 2 1 , 3 1 3 2 , 3 1 3 13 , 3 1 ( 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 1 1 1 1 [ AIEEE 2003 ]
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