Question

A weather forecast predicts that for each day from Monday to Friday this week, there is a $40\%$ chance of sun, a $25\%$ chance of getting 4 inches of rain, and a $35\%$ 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

Answer 1

To find the expected total rainfall from Monday to Friday, multiply the expected rainfall per day (4.5 inches) by the number of days (5), resulting in a total expected rainfall of 22.5 inches for the week.

Step-by-step explanation:

The expected value of the total number of inches of rain that will fall from Monday to Friday can be calculated using the concept of expected value in probability. We multiply each outcome by its respective probability and sum these products. There are two outcomes for rainfall: 4 inches and 10 inches, each with their given probabilities.

Calculation of expected rainfall per day:

• 4 inches of rain has a probability of 25%, or 0.25.
• 10 inches of rain has a probability of 35%, or 0.35.

Daily expected rainfall = (4 inches * 0.25) + (10 inches * 0.35) + (0 inches * 0.40) = 1 inch + 3.5 inches + 0 inches = 4.5 inches.

To find the expected value for the week, we multiply the daily expected amount by the number of days in the week (5 days).

Weekly expected rainfall = 4.5 inches/day * 5 days = 22.5 inches.