Please explain each solution using probability rules. As part of a promotional s
ID: 3206999 • Letter: P
Question
Please explain each solution using probability rules. As part of a promotional scheme, the manufacturer of a new breakfast food offers a prize of $100,000 to someone willing to try the new product (distributed without charge) and send in his or her name on the label. The winner is to be drawn at random from all the entries received. If 300,000 people enter the contest, what are the expected winnings per entrant? ****All parameters must be calculated from scratch using the appropriate probability distribution. Do not use short-cut formulas such as the ones for the mean and variance of a binomial distribution. For some problems you may need to construct the probability distribution before you can calculate parameters. All probabilities must be calculated from first principles, as in the first homework assignment. DO NOT use short-cut formulas, such as the binomial equation.Explanation / Answer
ans=
On a conceptual level, 300,000 people enter the raffle: one is the winnerand the other 299,999 (= 300,000 - 1) are losers.The one winner gets theentire $100,000 and all the others get nothing.With this understanding ofthe situation, use the expected value equation in section 5.3:There is oneterm with value x*prob(x) = $100,000*(1/300,000) = $100,000/300,000 =$0.3333.All the other terms x*prob(x) are $0*(1/300,000) = 0.Adding allthese terms gives the expected value of $0.3333
More precisely, the expected value is calculated as[x*prob(x)].Let X bethe rv of cash prize from the raffle. If your name is drawn, then you win$100,000; if your name isn't drawn, you win nothing. As a result, there areonly two values for the rv: x = $100,000 and x = $0.The expected value is calculated as follows:
x, $ prob(x) E(x),
$100,000 1/300,000 100,000/340,000 = 0.3333333
1/300,000 0 0
1/300,000 0... ... .. 0
1/300,000 0 (299,999 0's) 0.333333So the expected value is $0.33333 or 33.33 cents