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# HW5 - is the probability that each student gets at least...

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CSE21 FA11 Homework #5 (10/24/11) 5.1. (a) 10 cards are drawn at random one at a time with replacement from an ordinary deck of cards.What is the sample space? What is the probability that no Ace appears on any of the draws? What is the probability that at least one King appears in 10 draws? What is the probability that at least 2 Queens appear in the 10 draws? (b) What are the corresponding probabilities in (a) if the drawing is done without replacement ? 5.2. Let A and B be events with Pr ( A ) = 3 7 , Pr ( B ) = 1 2 and Pr (( A B ) c ) = 3 8 . What is Pr ( A B )? 5.3. A fair coin is flipped 10 times. What is the probability that there are at most two heads? 5.4 A biased coin has Pr ( Heads ) = α and Pr ( Tails ) = 1 - α . The coin is flipped 3 times. What is the most likely number of Heads to appear (as a function of α )? 5.5 12 identical jellybeans are distributed randomly to 5 students. What
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Unformatted text preview: is the probability that each student gets at least one jellybean? What is the probability that each student gets at least two? 5.6 A bin at Blockbuster contains 100 DVD’s of which 20 are defective. You randomly select 10 and try them out at home. You discover that there 2 defective DVD’s in the 10 that you selected. The store now allows you to select 2 replacements from the same bin (which now only has 90 DVD’s in it, since you already removed 10). What is the probability that none of 10 DVD’s you ﬁnally end up with are defective? What is the answer to this question if you ﬁnd k defectives in your initial choice? 1...
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