About 1 in 300 births leads to identical twins whereas about

About 1 in 300 births leads to identical twins, whereas about 1 in 125 births leads to fraternal twins. Assuming that it is equally like to have a boy or a girl, set up a probability model for a birth event and answer the following: (a) What is the probability to have a single child that is a boy? (b) What is the probability to have twins that are both boys? (Hint: A probability tree may help) (c) Elvis had a twin brother who died at birth. What is the probability that Elvis was an identical twin?

Solution

a)

P(single) = 1 - P(twin) = 1- [1/300 + 1/125] = 0.98866666

Thus,

P(single and boy) = P(single) P(boy|single)

= 0.9886666(1/2)

= 0.4943333 [answer]

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b)

For fraternal twins, there are 4 results:

BB
GB
BG
GG

Thus, P(BB|fraternal) = 1/4.

Thus,

P(twins and both boys) = P(identical) P(both boys|fraternal) + P(fraternal) P(both boys|fraternal)

= (1/300)(1/2) + (1/125)(1/4)

= 0.003666666667 [ANSWER]

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c.

P(identical twin|twin) = P(identical) / P(twin) = (1/300) / (1/300 + 1/125) = 0.29412 [ANSWER]