1. Suppose a die is tossed twice. Define N = {(x, y) | x, y E {1,2,3, 4, 5, 6}}. Let Pmn be the set of outcomes where m dots appear on the nth toss. Write the following events in terms of Pmn and only these set operations (complementation, union, intersection) A = event where five dots appear in only one toss B = event where two dots appear in the third toss only C = event where five dots appear in at least one toss D = event where five dots appear in both tosses E = event where five dots do not appear at all

Use the table below for groups of 8 births from 8 different sets of parents. Number of girls, x P(x) 0 0.004 1 0.031 2 0.109 3 0.219 4 0.273 5 0.219 6 0.109 7 0.031 8 0.004   Find the probability of getting exactly 7 girls in 8 births.

A card is randomly drawn from a deck of well-shuffled playing cards. Let event E be that the card is a king and event F be that the card is a diamond. A standard 52-card deck is split evenly into four suits of cards (hearts, diamonds, clubs, and spades). Each suit contains the cards ace, 2, 3.., 10, jack, queen, king. a) Find P(E) and P (E'). b) Find P(F) and P (F'). c) Find P(EUF).