I have a standard deck of playing cards with 52 cards. Suppose that I let you gu

Question

I have a standard deck of playing cards with 52 cards. Suppose that I let you guess n cards, and if those are the first n cards that I pick from the shuffled deck, then I pay you $X. We will assume the the order doesn’t matter, for example if n = 2 and you guess Jack of Diamonds and Ace of Spades, then as long as I draw those two cards, it doesn’t matter what order they show up. To play this game, you have to pay me $1. For each value of n = 1, 2, 3, 4, 5, 53, 51, 52, answer the following questions, (a) What is the probability of winning $X? (b) How high would X have to be to make your expected value of the bet equal to the cost of participating ($1)? (Hint: If n = 4, then X = $270, 725)

Explanation / Answer

the following table shows the the probability of winning $X and the amount high that would X have to be to make expected value of the bet equal to the cost of participating $1

n combinations Probability X- Amount high to make expected value of the bet equal to the cost of participating $1 1 52 0.019230769 $                                                     52 2 1326 0.000754148 $                                               1,326 3 22100 4.52489E-05 $                                             22,100 4 270725 3.69379E-06 $                                          270,725 53 0 0 $                                                      -   51 52 0.019230769 $                                                     52 52 1 1 $                                                       1

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