4. Subjective Probability Use subjective judgment to estimate the probability that the next time you ride an elevator, it gets stuck between floors.

1>2, 1>20,358, 146 Chapter 4 Probability EXAMPLE If you bet $5 on the number 13 in roulette, your probability of winning is and the payoff odds are given by the casino as 35:1.

a. Find the actual odds against the outcome of 13.

b. How much net profit would you make if you win by betting on 13?

c. If the casino were operating just for the fun of it, and the payoff odds were changed to match the actual odds against 13, how much would you win if the outcome were 13?

SOLUTION

a. With and we get

b. Because the payoff odds against 13 are 35:1, we have so that there is a $35 profit for each $1 bet. For a $5 bet, the net profit is

$175. The winning bettor would collect $175 plus the original $5 bet. That is, the winning bettor of $5 would receive the $5 bet plus another $175.

The total amount returned would be $180, for a net profit of $175.

c. If the casino were operating for fun and not for profit, the payoff odds would be equal to the actual odds against the outcome of 13. If the payoff odds were changed from 35:1 to 37:1, you would obtain a net profit of

$37 for each $1 bet. If you bet $5, your net profit would be $185. (The casino makes its profit by paying only $175 instead of the $185 that would be paid with a roulette game that is fair instead of favoring the casino.)

35:1 5 snet profitd:samount betd actual odds against 13 5 Psnot 13d Ps13d 5

37>38 1>38 5

37 1

or 37:1 Ps13d 5 1>38 Psnot 13d 5 37>38, 1>38 In Exercises 5 and 6, express the indicated degree of likelihood as a probability value between 0 and 1.