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prob2sol

# prob2sol - The Hong Kong University of Science and...

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Page 1 of 4 The Hong Kong University of Science and Technology ISMT 111 - Business statistics, Fall 2002 Problem Sheet 2 Solutions 1. Let A and B be the event that A - Employee favors a buyout B - Employee will retire within the next 15 years (a) P( A ) = 0.382 (b) P( B ) = 0.379 (c) P( A|B ) = 0.55 (d) Since P( A | B ) P( A ), the two events A and B are dependent. In other words, an employee’s attitude towards the buyout is dependent on his or her retirement plan. 2. (a) Let T be the event that the chosen coin is two-headed P( T ) = 1/10 = 0.1 (b) Let T be the event that the chosen coin is two-headed and X be the number of heads obtained in 3 trials. Pr( X = 1) = 0.3375 (c) Probability of getting 2 heads from the coin tossing experiment: Pr( X = 2) = 0.3375 (d) Probability distribution for the number of heads obtained from the experiment. Pr( X = 0) = 0.1125 Pr( X = 3) = 0.2125 The distribution of X is given by x 0 1 2 3 P(x) 0.1125 0.3375 0.3375 0.2125 (e) Mean and Standard deviation of the above distribution: μ = 1.65, s = 0.9367 (f) Probability that the chosen coin is two-headed, given the results of the experiment are all heads: Pr( T | X = 3) = 0.4706 (g) If the chosen coin is tossed a million times and the result are all heads, 1 ) 1000000 | Pr( = = X

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prob2sol - The Hong Kong University of Science and...

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