Follow these steps. a) Define a probability space (2, F, P) that models the gend

Question

Follow these steps. a) Define a probability space (2, F, P) that models the gender distribution of two siblings. Assume that the two genders are equally likely and independent b) Given that you know that one of the two siblings is male, determine the probability that he has a sister and the probability that he has a brother. Try to follow this procedure: i) define an event A that represents that at least one of the two siblings is male; ii) define a second random variable B that represents the two siblings have opposite gender; ii) compute P(B|A)

Explanation / Answer

a) for two genders Male M and Female F are equally likely

sample space S ={ MM, MF , FM , FF}

b) i) event A ; sample space = (at least one is male) ={ MM,MF, FM} (at least one is male)

P(A) =3/4 as there are 3 events out of total sample space of 4 outcomes

event B, sample space =both siblings have opposite gender ={ MF ,FM}

hence P(B) =2/4 =1/2

(iii) P(B|A) =P(A and B)/P(B)

number of events in P(A and B) ={ MF , FM} =P(B)

hence P(B|A) =P(A and B)/P(B) =(1/2)/(3/4) =2/3

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