math 411 homework5

# math 411 homework5 - 10 of the time when he takes the...

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Department of Mathematics Fall 2011 Volodymyr Nekrashevych Math 411 — Problem Set 5 Issued: 10.08 Due: 10.14 5.1. Two events have P ( A ) = 1 / 4, P ( B | A ) = 1 / 2, and P ( A | B ) = 1 / 3. Compute P ( A B ), P ( B ), and P ( A B ). 5.2. A friend ﬂips two coins and tells you that at least one is head. Given this information, what is the probability that the ﬁrst coin is head? 5.3. An urn contains 8 red, 7 blue, and 5 green balls. You draw out two balls and they are of diﬀerent color. Given this, what is the probability that they are red and blue? 5.4. John takes the bus with probability 0.3 and the subway with proba- bility 0.7. He is late 40% of the time when he takes the bus, but only
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Unformatted text preview: 10% of the time when he takes the subway. What is the probability that he is late for work? 5.5. Two hunters shoot at a deer, which is hit by exactly one bullet. If the ﬁrst hunter hits his target with probability 0.3 and the second with probability 0.6, what is the probability that the second hunter killed the deer? 5.6. Three bags lie on the table. One has two gold coins, one has two silver coins, and one has one silver and one gold. You pick a bag at random, and pick out one coin. If this coin is gold, what is the probability that you picked the bag with two gold coins....
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