Homework Help: Mathematics for Liberal Arts

Posted by Sasha on Sunday, October 24, 2010 at 12:30am.

Each round of the game costs $1 to play. A round consists of you choosing a number from 1 to 10 and then picking a card at random from a standard deck of cards. I fyou pick a card with the number you chose, you win $5. If you don't, you lose your dollar.
a) What is the probability that you can win? What is the probability you can lose?

Mathematics for Liberal Arts - Sasha, Sunday, October 24, 2010 at 12:59am
Using a standar deck of 52 cards, what is the probability of drawing four cards of the same number(eg.four aces, 4 kings, fiyr 2s, four 3s,etc?
Mathematics for Liberal Arts - drwls, Sunday, October 24, 2010 at 1:03am
The probability of winning is obviously 1/10 and the probability of losing is 1 minus that (9/10). Those are not the important numbers. What matters is the expected gain or loss, taking the amount of the "pot" into account..

There is a 1/10 chance of winning $5 (and your dollar back, presumably). That is an average return of 0.60, but there is a $1 cost to play each time, so on the average 40 cents is lost each time.

The expected return is a 40 cent loss per round. Those are pretty bad odds for the bettor.

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