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NO LINKS!! Please help me with this probability question​

NO LINKS!! Please help me with this probability question​-example-1

1 Answer

3 votes

Answer: b) not independent

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Step-by-step explanation:

Define these two events

A = father born in Michigan

B = mother born in Michigan

The notation ~A and ~B represent the opposite of each defined event above.

According to the table

P(A) = 0.48

P(B) = 0.73

If A and B were independent, then P(A and B) = P(A)*P(B) = 0.48*0.73 = 0.3504 = 35.04% but this contradicts the 29% in the "father born in Michigan" column and "mother born in Michigan" row. The table states that P(A and B) = 0.29 should be the case instead of 0.3504.

Because of this contradiction, this means P(A and B) = P(A)*P(B) is false and therefore A and B are NOT independent

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Another way to look at it:

P(A) = 0.48

P(A given B) = P(A and B)/P(B)

P(A given B) = 0.29/0.73

P(A given B) = 0.39726 approximately

If A and B were independent, then P(A) and P(A given B) would be the same value. However, they are not. This is another way to see why the events are NOT independent

Through similar calculations, P(B given A) = P(A and B)/P(A) = 0.29/0.48 = 0.6042 approximately which doesn't match with P(B) = 0.73; if A and B were independent then P(B) needs to be equal to P(B given A).

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