There is a $20 \%$ chance that next year the total number of employees in the office supply stores of a chain in Milwaukee will increase by 400 . There is a $70 \%$ chance that the increase will be 600 employees, and a $10 \%$ chance the total number of employees will decrease by 700 . Determine the expected gain or loss in the number of employees for next year.
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. There is an expected loss of $\square$ employees.
B. There is an expected gain of $\square$ employees.
C. There is neither an expected gain nor an expected loss.
Answer
\(\boxed{\text{{B. There is an expected gain of 430 employees.}}}\)
Step 1 ：Define the outcomes and their probabilities. The outcomes are 400, 600, and -700, with probabilities of 0.2, 0.7, and 0.1 respectively.
Step 2 ：Calculate the expected gain or loss by multiplying each outcome by its probability and summing the results. This can be represented as \( \sum \text{{outcome}} \times \text{{probability}} \).
Step 3 ：The result of the calculation is 430.0, which means there is an expected gain of 430 employees next year.
Step 4 ：\(\boxed{\text{{B. There is an expected gain of 430 employees.}}}\)
