A tough probability/percentages question!?

Question

According to a survey, the probability that residents owning 2 cars if annual household income is over 25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents do not own 2 cars if annual household income is not over $25,000?

How can we compute this?

Answer 1

Whenever I have a percentages question like this, I first always change the percents to actual numbers of people. That way it makes these numbers sound concrete. For convenience, let's say 100 people were surveyed.

Now I would draw a venn diagram with two intersecting circles. One circle is the group of people who makes $25,000+. The other circle is the group of people who own two cars. This means the intersecting region is the group of people who make $25,000+ and own 2 cars.

You know for sure that there are 60 people in the entire circle for the $25,000+, including the intersection of these two circles. Now 80% of those 60 people that make $25,000+ own 2 cars. That makes 48 people in the intersection region who fit both descriptions. Through subtraction, 12 people are in the rest of the $25,000+ circle. With similar logic, 70 people are in the entire 2 cars circle, so since 48 are already counted in the intersection, there must be 22 people left in the 2 cars circle. Adding up these numbers gives you 22 + 48 + 12 = 82 people. But we had a total of 100 people; where are the rest? The missing 18 people must fit your description of not owning 2 cars and not makeing $25,000+.

Answer 2

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Answer 3

One thing that I know that might help. That u cannot average with other averages or percent. To get it right u must change the numbers back to the original sample .