Solutions to Exam 1, Ma441,Spr05.

Solutions to Exam 1, Ma441,Spr05. - 1(15 points In the CASH...

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. 1. (15 points) In the CASH 5 Colorado Lottery, one chooses 5 numbers from the field 1 through 32. It costs \$1 per play. Twice a week 5 numbers are drawn without replacement from the field 1 through 32 and an individual's winnings are determined by the number of matches of his/her choices with those drawn. The table below lists the prizes that can be won (excluding the cost of the game): # Matches Prize 5 of 5 Jackpot = \$20,0001 4 of 5 \$200 3 of5 \$10 2 of5 \$1 a. In one play, what is the chance that an individual wins the Jackpot? . b.1n oneplay, what is the chance that an individual wins \$10 (for net winnings of\$9)? ~. In both parts, it suffices to express your an,swers in terms of unevaluated binomial coefficients. . I (i. Pi l1)/,J.s 111cJC.f;tJr);: --- co,... ('3 '\$') / b. P(WIJJ.5 \$/v) := (~)(2~) - ( 3"2- ) 2- '? .3 I If more than 10 tickets win the top prize in a singleCASH 5 drawing, the top prize will become parimutuel and all top prize winners will receive an equal share of \$200,000. .. 2

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. " " 2. (20 pts.) Suppose the chance of rain Tuesday is .45, and the chance of rain Wednesday' is .35. Also suppose the chance it rains on at least one of these
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