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# determining the probability of success at a game show

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In the final round of a TV game show, contestants have a chance to increase their current winnings of \$1million to \$2million. If they are wrong, their prize is decreased to \$500,000. A contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?

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#### Solution Preview

Hello,

In such a case as this, we calculate by multiplying the result by the percent possible it would happen. The equation would look like this:

50% chance of increasing money by \$1 million
and
50% chance of losing \$500,000
or to put it in mathematical terms:

0.50 X +\$1,000,000 = \$500,000
0.50 X -\$500,000 = \$250,000

So, it makes sense to play. The question of what is the lowest probability of success would still make the play profitable can be answered as follows:

P (probability percent) = ...

#### Solution Summary

The teacher shows how to determine what the lowest probability of success compared to the highest probability of failure that would make sense to participate in such a game.

\$2.19