Recent developments appear to make it possible for couples to dramatically incre

Question

Recent developments appear to make it possible for couples to dramatically increase the likelihood that they will conceive a child with the gender of their choice. In a test of a gender-selection method, 5 couples try to have baby girls a.If this gender-selection method has no effect, what is the probability that the 5 babies will be all girls? The probability is (Type an integer or a simplified fraction.) b. If there are actually 5 girls among 5 children, does this gender-selection method appear to be effective? Why? O A. Not necessarily, although the event is unusual it is not so improbable that the only reasonable explanation is the gender-selection procedure. B. Not necessarily, because the event of getting 5 females by chance is not unusual C. No, the gender-selection procedure cannot have any effect on the genders of the 5 children.

Explanation / Answer

Part a

We have to find P(X=5)

We are given n = 5

Probability of baby girl = p = 0.5

We are given that gender selection method has no effect.

P(X=x) = nCx*p^x*(1 – p)^(n – x)

P(X=5) = 5C5*0.5^5*(1 – 0.5)^(5 – 5)

P(X=5) = 1*0.5^5*0.5^0

P(X=5) = 1* 0.03125*1

P(X=5) = 0.03125

The probability is 3%.

Part b

Correct Answer: A

Not necessarily, although the event is unusual it is not so improbable that the only reasonable explanation is the gender selection procedure.

(We get probability 0.03125 which is less than 0.05; we say probability is unusual if it is less than 0.05.)

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