Question 190:

Asked on May 12, 2008

Tags: Addition Rule , Mutual Exclusive

1

Answer:

No answer provided yet.

I've coded your date into the contingency table below.

Electric Usage kWh	Single Family	Multi- Family	Total
< 5,000	15	25	40
5,000 – 7,000	35	15	50
7,000 – 11,000	65	15	80
11,000 – 15,000	25	5	30
Total	140	60	200

For question a) there were 80 households that had electric usage between 7000-1100kWh out of a total 200 households, giving the probability of 80/200 = .40.

For part b) the probability of selecting someone who uses less that 5000kwh is 40/200 = .20.

For part c) the use of the word OR indicates we need to add probabilities (the addition rule), the next question is if the events can happen at the same time (mutual exclusivity). Since you can be both a single-family home and use between 5,000 and 7,000 kWh, there is not mutual exclusivity. To take that into account, we calculate the individual probabilities, then subtract their joint probability. The probability of a single family dweller is 140/200 =.70. The probability of kWh usage between 5,000 and 7,000 is 50/200 = .25.  The probability of their joint occurrence is the cell in the table for both Single Family and 5000-7000kWh = 35/200 = .175.  So (.70 + .25)  - .175 = .775.