Question

8 black, 10 white. What's the expected value of the number of consecutive pairs containing different colors?

a. 4
b. 5
c. 6
d. 7

Answer 1

To find the expected value of the number of consecutive pairs containing different colors, we calculate the probability of each possible outcome and multiply it by the number of consecutive pairs in that outcome. The expected value is 4.

Step-by-step explanation:

To find the expected value of the number of consecutive pairs containing different colors, we can calculate the probability of each possible outcome and multiply it by the number of consecutive pairs in that outcome. In this case, there are 8 black and 10 white cards, so we can have a consecutive pair of colors in either of these two scenarios:

1. A black card followed by a white card
2. A white card followed by a black card

To calculate the probability of each scenario, we divide the number of favorable outcomes (7 for scenario 1 and 8 for scenario 2) by the total number of possible outcomes (17). The expected value is then calculated by multiplying each probability by the number of consecutive pairs in that scenario and adding them up. In this case, the expected value is 4. We can conclude that the answer is option a. 4.