Question

we have two urns. you can't tell them apart from the outside, but one has four $2 chips and six $10 chips, and the other has nine $2 chips and one $10 chip. you randomly draw a chip from one of the urns and it happens to be a $2 chip. without replacing this draw, i offer you a chance to draw and keep a chip from either urn. suppose you draw from the urn such that you maximize your expected earnings. what is the expected value of the chip you draw?

Answer 1

To maximize expected earnings after drawing a $2 chip without knowing from which urn it was, calculate the remaining chips in both urns and their respective expected values. Choose the urn with the higher expected value, which in this case is approximately $6.67 from the first urn.

Step-by-step explanation:

To calculate the expected value of the chip you draw after the initial $2 chip draw, we must first assess the remaining chips in each urn. Since we don't know from which urn the $2 chip was drawn, we have to consider both scenarios:

1. First urn (4 $2 chips and 6 $10 chips): After removing one $2 chip, there are 3 $2 chips and 6 $10 chips left, giving a total of 9 chips. Thus, the probability of drawing a $2 chip is 3/9, and the probability of drawing a $10 chip is 6/9.
2. Second urn (9 $2 chips and 1 $10 chip): After removing one $2 chip, there are 8 $2 chips and 1 $10 chip left, giving a total of 9 chips. Thus, the probability of drawing a $2 chip is 8/9, and the probability of drawing a $10 chip is 1/9.

We now calculate the expected value (EV) for both scenarios:

• First urn EV = (3/9) * $2 + (6/9) * $10 = $6.67
• Second urn EV = (8/9) * $2 + (1/9) * $10 = $2.89

Since the expected value from the first urn is higher, you should choose to draw from the first urn to maximize your expected earnings. The expected value of the chip you draw from the first urn will be approximately $6.67.