Question

A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 70% of the time and a European business makes a profit 80% of the time. If there are 1050 American businesses and 1040 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?

Answer 1

Solution:

We are given:

American business on the stock index makes a profit 70% of the time.

European business makes a profit 80% of the time.

There are total 1050 American businesses in the stock index and 1040 European businesses in the stock index.

Now the expected number of businesses in the stock index to make a profit is:

Therefore, the expected number of businesses in the stock index to make a profit is 1567