The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by A, B, and C. Let
P(A) 5 p1, P(B) 5 p2, and P(C) 5 p3. In n independent trials, the probability of x1
outcomes of type A, x2 outcomes of type B, and x3 outcomes of type C is given by
A genetics experiment involves six mutually exclusive genotypes identified as A, B, C, D, E, and F, and they are all equally likely. If 20 offspring are tested, find the prob- ability of getting exactly five A's, four B's, three C's, two D's, three E's, and three F's by expanding the above expression so that it applies to six types of outcomes instead of only three.
minimum usual value 5 M 2 2S
States Rig Lot- tery Selections
Many states run a lottery in which players select four digits, such as 1127 (the author's birthday). If a player pays $1 and selects the win- ning sequence in the correct order, a prize of $5000 is won. States monitor the number selections and, if one particular sequence is selected too often, players are pro- hibited from placing any more bets on it. The lottery machines are rigged so that once a popular sequence reaches a certain level of sales, the machine will no longer accept that particular sequence. This prevents states from paying out more than they take in. Critics say that this practice is unfair. Ac- cording to William Thompson, a gambling expert at the University of Nevada in Las Vegas, "they're saying that they (the states) want to be in the gambling business, but they don't want to be gam- blers. It just makes a sham out of the whole numbers game."