homework1

# homework1 - (a the older child is a boy and(b atleast one...

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1 EL 630: Homework 1 1. A fair die is rolled twice. For this experiment, define events A and B such that the events are (a) disjoint (mutually exclusive), but not independent (b) independent but not mutually exclusive (c) independent and mutually exclusive (d) neither independent nor mutually exclusive. 2. If 4 / 1 ) ( , = A P B A and , 5 / 2 ) ( = B P find ) | ( B A P and ). | ( A B P 3. Consider a game which consists of two successive trials. The first trial has outcomes A or B and the second outcomes C or D . The probabilities for the four possible outcomes of the game are as follows . 3 1 ) , ( ; 6 1 ) , ( ; 6 1 ) , ( ; 3 1 ) , ( = = = = D B P C B P D A P C A P Are A and C statistically independent? Prove your answer. 4. Consider a family with two children of different ages. Assume each child is as likely to be a boy as it is to be a girl. What is the conditional probability that both children are boys, given that
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Unformatted text preview: (a) the older child is a boy and (b) atleast one of the children is a boy. 5. A box contains 1000 light bulbs. The probability that there is atleast 1 defective bulb is 0.1, and the probability that there are atleast 2 defective bulbs is 0.04. Find the probability in each of the following cases (a) the box contains no defective bulb (b) the box contains exactly one defective bulb (c) the box contains at most one defective bulb. 6. A group of students consists of 60% men and 40% women. Among the men 30% are blond while among the women, 40% are blond. A person is chosen at random from the group and is found to be blond. Use Bayes’ formula to compute the probability that the person is a man....
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## This note was uploaded on 04/24/2011 for the course ECE 6303 taught by Professor Voltz during the Spring '11 term at NYU Poly.

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