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HW02 - is chosen at random What is the probability of this...

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STAT 36-217, HW 2, due Thursday 09/10/2009, 10:30 AM 1. Suppose P ( B ) > 0. Show that P ( A B | B ) = P ( A | B ). 2. Roll two fair dice, what is the probability that the sum is 2 , 3 , . . . , 12? 3. Two dice are rolled. What is the probability that at least one is a six? 4. Roll two dice. What is the conditional probability that the first dice is a six given that the sum of the dice is 7 , 8 , 9? 5. Urn 1 has 5 white and 7 black balls, Urn 2 has 3 white and 12 black balls. We flip a coin. If the outcome is heads, then a ball is selection from Urn 1, otherwise from Urn 2. Suppose a white ball is selected. What is the probability that the coin landed tails? 6. Assume that each child who is born is equally likely to be a boy or a girl. If a family has two children, what is the probability that both are girls given that (a). the elder is a girl, (b). at least one is a girl. 7. 5% men are color-blinded, and 25% women are color-blinded. A color-blinded person
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Unformatted text preview: is chosen at random. What is the probability of this person being male? Assume that there are equal numbers of males and females. 8. 60% of the families in a certain community own their own car, 30% own their own home, and 20% own both their own car and their own home. If a family is chosen at random, what is the probability owns a car or a house but not both? 9. Toss coin for three times. Let A i be the event that we get the same outcome in the two tosses excluding the i-th one, 1 ≤ i ≤ 3 (i.e. A 1 is the event that we get the same outcomes in the second and the third tosses; similar for A 2 and A 3 ). Show that A i are pairwise independent but not independent. 10. In a class there are 4 freshmen boys, 6 freshman girls, and 6 sophomore boys. How many sophomore girls must be present if sex and class are to be independent when a student is selected at random. 1...
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