Chapter 6.1 review questions, #23 part B. In order to find the probability of a fourth...

Chapter 6.1 review questions, #23 part B. In order to find the probability of a fourth or fifth live birth, I have to multiple the probability of a fourth birth and the probability of a fifth birth. This would be 0.096 x 0.047. My calculator is saying the answer is 0.004512. However, Chegg textbook solutions and the book says the answer is 0.143, which would be the two probabilities being added together. I'm not sure which is wrong; is the answer wrong or is the operation wrong?

Expert Solution

The question is:

To find the probability of a fourth live birth or fifth live birth:

Addition Theorem of Probability is used as follows:
P(A + B) = P(A) + P(B)

where

A = fourth live birth

B = fifth live birth

By definition of Addition of Probability Theory:
P(A + B) = Probability of A or B.

Thus,

Using Addition Theorem of Probability :
P( fourth live birth or fifth live birth) = P( fourth live birth) + P(fifth live birth)

= 0.096 + 0.047

= 0.143

We have to multiply P(A) and P(B) only when we require the probability of both A and B.

i.e.,

By Multiplication Theorem of Probability:
P(A and B) P(A) X P(B)

Since here we require the probability of A or B, only Addition Theorem of Probability is to used.

orchestra answered 1 year ago

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