A gambler is trying to determine whether or not to make a bet. If he bets and wins, he will profit $2000. If he bets and loses, he has to pay $300. The probability that he wins the bet is 15%. Find the gambler's expected value if he makes the bet.

The gambler's expected value if he makes the bet is $45.

Step-by-step explanation:

Expected value:

15% probability of a profit of $2000.

100 - 15 = 85% probability of having to pay $300, that is, a loss of $300.

The expected value is each outcome multiplied by it's probability, so:

The gambler's expected value if he makes the bet is $45.