Question

Evan is an entrepreneur. He plans to start 2 different very small businesses in the next year. Both businesses are independent of each other, and each business has an 85% chance of being successful and a 15% chance of failing. Each business will make Evan $500 if it succeeds or lose $500 if it fails. If X is a random variable that represents Evan's profit from starting these 2 businesses, what are the probabilities for all possible values of X. P(X) = {-$1000, $0, $1000} =

a. 0.1275, 0.7225, 0.15
b. 0.15, 0.7225, 0.1275
c. 0.1275, 0.15, 0.7225
d. 0.7225, 0.1275, 0.15

Answer 1

To calculate the probabilities for all possible values of X in Evan's business ventures, we need to consider different combinations of success and failure for each business. The probabilities for X being -$1000, $0, and $1000 are 0.0225, 0.255, and 0.7225 respectively.

Step-by-step explanation:

To calculate the probabilities for all possible values of X, we need to consider all the different combinations of success and failure for the two businesses. Let's go through each possibility step by step:

1. Both businesses succeed: The probability of this is 0.85 * 0.85 = 0.7225. The profit in this case would be $500 + $500 = $1000.

2. The first business succeeds and the second business fails: The probability of this is 0.85 * 0.15 = 0.1275. The profit in this case would be $500 - $500 = $0.

3. The first business fails and the second business succeeds: The probability of this is 0.15 * 0.85 = 0.1275. The profit in this case would be -$500 + $500 = $0.

4. Both businesses fail: The probability of this is 0.15 * 0.15 = 0.0225. The profit in this case would be -$500 - $500 = -$1000.

Therefore, the probabilities for all possible values of X are:

P(X = -$1000) = 0.0225

P(X = $0) = 0.1275 + 0.1275 = 0.255

P(X = $1000) = 0.7225