A weather forecast predicts that for each day from Monday to Friday this week, there is a 40% chance of sun, a 20% chance of getting 4 inches of rain, and a 40% chance of getting 10 inches of rain. What is the expected value of the total number of inches of rain which will fall from Monday to Friday? Give your answer as a decimal rounded to the nearest tenth.
Since your week is $5$ days, and there is a $40\%$ chance of sun, we can say that "we expect" $2$ days to have sun. Now, since we have a $20\%$ chance of $4$ inches of rain, we can "expect" $1$ day to have $4$ inches of rain. Now, we have a $40\%$ chance of $10$ inches of rain, hence the last $2$ days we "expect" to have $10$ inches of rain. Now we have $4+10+10=24$ inches of rain from Monday to Friday. This is my take on this problem. Please tell me if this is wrong or does not satisy your problem so I can review and revise.