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[Solution Library] Approximately one-third of all human twins are identical (one-egg) and two-thirds are fraternal (two-egg) twins. Identical twins are

Question: Approximately one-third of all human twins are identical (one-egg) and two-thirds are fraternal (two-egg) twins. Identical twins are necessarily the same sex, with male and female being equally likely. Among fraternal twins, approximately one-fourth are both female, one-fourth are both male, and half are one male and one female. Finally, among all U.S. births, approximately 1 in 90 is a twin birth. Define the following events:

\[\begin{aligned} &A=\{\mathrm{a} \text { U.S. birth results in twin females }\} \\ &B=\{\mathrm{a} \text { U.S. birth results in identical twins }\} \\ &C=\{\text { a U.S. birth results in twins }\} \end{aligned}\]
  1. State, in words, the event \(A \cap B \cap C\).
  2. Find \(P(A \cap B \cap C)\).

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