HW due Thursday 9/13 September 12 2011 1. The probabili

HW due Thursday 9/13 September 12 2011 1. The probability that a visit to a primary care physicians (PCP) oce results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCPs oce 30% are referred to specialists and 40% require lab work. Determine the probability that a visit to a PCPs oce results in both lab work and referral to a specialist. 2. deGroot 1.12 #2 If ABC are three events such that P(A [ B [ C) = :7 what is P(Ac Bc Cc)? 3. deGroot 1.12 #6 Suppose a box contains r red and w white balls. Sup- pose balls are draw one at a time without replacement . (a) What is the probability that all red balls will be obtained before any white balls ? (b) What is the probabilty that all red balls will be obtained before 2 white balls ? 4. from Quant Job Interview:Consider a deck of 52 cards ordered with A > K > Q > ::: > 2. I draw a card and you draw a card. What is the probability that my card is bigger than yours ? Remark: ties may occur. 5. What is the probability that a 5 card poker hand contains (exactly) 2 pairs ? What is the probability that all ve card come from the same suit ? 6. In a well shued deck of cards what is the probability that that the 2nd and fourth cards are aces ? 7. Find Pj=n j=0 j??njusing generating functions.Hint: dierentiate P??njxj . 1
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