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# Help in probability theory, Bayes' theorem. Does Jane Doe own a car given these priors?

Let us say that 90% of left-handed American women own a car. Jane Doe belongs to that group. But we know something else. We know that Jane Doe owns a bicycle.

We also know that of left-handed American women who own cars, 10% also own a bicycle. Among those who don't own cars, 20% own a bicycle.

So, Jane is a left-handed American woman who owns a bicycle. What can we come up with about whether she owns a car?

Thanks.

### 2 Answers

- ?Lv 75 years agoFavorite Answer
A1 = 90% = 0.9

A2 = 100% - 90% = 10% = 0.1

P(B|A1) = 10% = 0.1

P(B|A2) = 20% = 0.2

Required probability = P(A1|B) = [0.9*0.1] / [0.9*0.1 + 0.1*0.2]

= 0.09 / 0.11

= 9/11

There is 9/11 chance that Jane owns a car

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- M3Lv 75 years ago
P(own bicycle & own car) = 10% of 90% = 9%

P(own bicycle & don't own car) = 20% of 10% = 2%

P(own car | owns bicycle) = 9/(9+2) = 9/11 <--------

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