Friday, October 24, 2014

College Algebra, Chapter 10, 10.5, Section 10.5, Problem 10

Find the expected value (or expectation) of the games described.

A card is drawn from a deck. You win $104 if the card is an ace, $26 if it is a face card, and $13 if it is the 8 of clubs.

The deck of 52 cards has four ace with probability 452=13, twelve face card with probability
1252=313 and one 8 of clubs with probability 152.
So you get $104 with probability 13,$26 with probability 318
and $13 with probability 152. Thus, the expected value is

104(113)+26(313)+13(152)=574=14.25

This means that if you play this game, you will make, $14.25 per game.

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