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Should You Play?

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Date: 08/07/97 at 22:29:16
From: Connie
Subject: Face card probability

A game consists of three cuts with a deck of 52 cards. You win \$1 if a
face card turns up on at least one cut, but you lose \$1 if a face card
does not turn up. Should you play? Why?

Thanks,
Connie
```

```
Date: 08/08/97 at 05:03:24
From: Doctor Anthony
Subject: Re: Face card probability

A game is considered fair if the expectation is zero.  That is, if in
a long series of games you would expect to break even.

The definition of 'expectation' if x1 occurs with probability p1,
x2 occurs with probability p2, and so on, is:

E(x) = p1.x1 + p2.x2 + p3.x3 + ...... + pn.xn

To find the probabilities of at least one face card in 3 trials,
consider instead the probability of no face card in 3 trials, and
subtract this probability from 1.

Probability of no face card in three trials = (9/13)^3 = .331816

Probability of at least one face card in 3 trials = 1 - (9/13)^3

= 0.66818
Your expectation = 1 x .66818 - 1 x .331816

= 0.33637

With a positive expectation you should certainly play.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Probability

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