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Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

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BuyFindarrow_forward

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Pregnancy test A self-administered pregnancy test detects 85% of those who are pregnant but does not detect pregnancy in 15%. It is 90% accurate in indicating women who are not pregnant but indicates 10% of this group as being pregnant. Suppose it is known that 1% of the women in a neighborhood are pregnant. If a woman is chosen at random from those living in this neighborhood and if the test indicates she is pregnant, what is the probability that she really is?

To determine

To calculate: The probability of selecting pregnant lady if the test indicates that she is pregnant when pregnancy test detects 85% of those who are pregnant and doesn't detect 15%. It is 90% accurate in detecting that a women are pregnant but indicates 10% of the non-pregnant group as pregnant and 1% women in the neighborhood are pregnant.

Explanation

Given information:

The provided information is:

A pregnancy test detects 85% of those who are pregnant and doesn't detect 15%. It is 90% accurate in detecting that a women are pregnant but indicates 10% of the non-pregnant group as pregnant.

It is also provided that 1% women in the neighborhood are pregnant.

Formula used:

Probability tree:

Every branched in the tree has probability, which is conditional probability that the specified event will take place where the condition is that the event on the preceding branches have occurred.

When an event can be described by one path by using the probability tree, the probability that the event will take place is the product of the probabilities on the branches along the path which represent the event.

The Bayes Formula and Trees:

Pr(E1|F1)=product of branch probabilities on a path leading toF1 through E1Sum of all branch products on paths leading to F1 

Calculation:

Consider the provided information:

A pregnancy test detects 85% of those who are pregnant and doesn't detect 15%. It is 90% accurate in detecting that a woman is pregnant but indicates 10% of the non-pregnant group as pregnant.

Where 1% women in the neighborhood are pregnant.

Now, draw the probability tree which states that,

Every branched in the tree has probability, which is conditional probability that the specified event will take place where the condition is that the event on the preceding branches have occurred.

When an event is described by using the probability tree, the probability that the event will take place is the product of the probabilities on the branches along the path which represent the event.

Therefore, the probability tree is,

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