# determining the probability of success at a game show

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.