SOLUTION: The probability that twins are identical is 0.4. While identical twins are always of the same sex, there is only a 48% chance that twins will be of the same sex if they are not ide

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Question 774258: The probability that twins are identical is 0.4. While identical twins are always of the same sex, there is only a 48% chance that twins will be of the same sex if they are not identical. We define the random variable X as follows:
X= 1 If we hav identical twins that are of the same sex
2 If we have identical twins that are of different sexes
3 If we have non-identical twins that are of the same sex
4 If we have non-identical twins that are of different sexes
a) Determine the probability mass function associated with the random variable defined as X.
b) Draw the p.m.f. of X.
c) Let A be the even that the twins are of the same sex. What is Pr(A)?
Answer by oscargut(2103) (Show Source):
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The probability that twins are identical is 0.4. While identical twins are always of the same sex, there is only a 48% chance that twins will be of the same sex if they are not identical. We define the random variable X as follows:
X= 1 If we hav identical twins that are of the same sex
2 If we have identical twins that are of different sexes
3 If we have non-identical twins that are of the same sex
4 If we have non-identical twins that are of different sexes
a) Determine the probability mass function associated with the random variable defined as X.
b) Draw the p.m.f. of X.
c) Let A be the even that the twins are of the same sex. What is Pr(A)?

Solution: (i do the first part)
a)
P(X=1) = 0.4
P(X=2) = 0
P(X=3) = 0.6(0.48)=0.288
P(X=4) = 0.6(0.52) = 0.312

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