At a charity bazaar it costs $2.00 to draw one card at random from an ordinary d

Question

At a charity bazaar it costs $2.00 to draw one card at random from an ordinary deck of 52 playing cards. If you draw an ace, you will be given a $10 bill, and if you draw a face card (jack, queen, or king) your $2 will be returned to you. What is the proprietor’s expected profit per customer?

RULES:

-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.

-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.

Explanation / Answer

here probability of drawing an ace =4/52 =1/13 (as there are 4 ace in a deck)

probability of drawing a face card =12/52=3/13 (as thre are 12 face cards)

therefore proprietor’s expected profit per customer =expected win from drawing an ace+expected win from drawing a face card- cost of ticket

=(1/13)*10+(3/13)*(2) -2 =$ -0.77

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