Question

EXPECTED VALUE

Do the following problems using the expected value concepts learned in this section

1) In a town, 40% of the men and 30% of the women are overweight. If the town has 46% men and 54% women, what percent of the people are overweight?

2) A game involves rolling a single die. One receives the face value of the die in dollars. How much should one be willing to pay to roll the die to make the game fair?

3) A game involves drawing a single card from a standard deck. One receives 60 cents for an ace, 30 cents for a king, and 5 cents for a red card that is neither an ace nor a king. If the cost of each draw is 10 cents, should one play? Explain.

4) During her four years at college, Niki received A's in 30% of her courses, B's in 60% of her courses, and C's in the remaining 10%. If A=4 B=3 and C=2 find her grade point average.

5) A Texas oil drilling company has determined that it costs $25,000 to sink a test well. If oil is hit, the revenue for the company will be $500,000. If natural gas is found, the revenue will be $150,000. If the probability of hitting oil is 3% and of hitting gas is 6%, find the expected value of sinking a test well.

6) Assume that for the next heavyweight fight the odds of Mike Tyson winning are 15 to 2. A gambler bets $10 that Mike Tyson will lose. If Mike Tyson loses, how much can the gambler hope to receive?

Answer 1

1) Proportion of people overweight is

The percent of the people are overweight is

2) Let be the outcome of the dice. Then

The expected value of the amount one receives is

To make the game fair, one should be willing to pay to roll the die for .

3) Probabilities are given below.

The expected amount earned of the game is

Since the cost of each draw is , one should play.

(The expected amount you earn is more than the cost).

4) Her grade point average is