A game of chance consists of drawing two cards at random from an ordinary deck o

Question

A game of chance consists of drawing two cards at random from an ordinary deck of 52 cards. If you draw a pair (that is, two cards of the same value), you win $120; if you don’t, you lose $10. The probability of drawing a pair is 0.059.

a. Let X = the amount that you can win. (note that this could be a negative amount.). Write down the probability mass function of X as a table.

b. Find the expected value of X. What does it tell you about a player’s prospects if he/she played the game repeatedly?

c. What would the winning amount (i.e. the $120) need to be changed to in order for you to break even in the long run? Assume that if you don’t draw a pair, you would still lose $10.

Explanation / Answer

a) from above below is probability mass function of X as a table:

b)  expected value of X =E(X)=120*0.059-10*0.9410 =$ -2.33

c)

winning amount to break even =0.9410*10/0.059=159.4915

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