Three couples and two single individuals have agreed to attend an investment sem

Question

Three couples and two single individuals have agreed to attend an investment seminar. Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both the people in the couple will be late or neither will be late). Assume that whether or not any particular couple or individual arrives late is independent of whether or not any other couple or individual does so. Let X = the number of people who arrive late for the seminar. Let F(x) be the cumulative distribution function of X, and determine F(4). Hint: For ease of explanation, label the three couples #1, #2, and #3, and the two individuals #4 and #5.

Explanation / Answer

X=0 or 1 or 2 or 3 or 4 or 5 This is a binomial experiment where p=.4,q=1-p=.6 F(4)=P(x=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) F(5)=1 sum of all possible outcomes F(4)=1-P(X=5) P(X=5) is all probability all late and they are independent so P(x=5)= .4^5=.010 F(4)=1-.010=.98976

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