(a) Make a histogram showing the probability distribution of the number of illiterate people out of the nine people in the sample.

Recall that the binomial distribution with parameters n, p, and r gives the probability distribution of the number of r successes in a sequence of n trials, each of which yields success with probability p.

Here we can let "success" be defined as "finding an illiterate person." We are given that 20% of all people in the United States are illiterate. Therefore, each person has a 20% chance of being illiterate, which means the probability of interviewing a person and finding them to be illiterate is 0.2. So, p=

In this survey, a random sample of nine people are interviewed, so n =

Recall that the complement rule gives the probability that an event will not happen. So the probability that a fisherman catches one or more fish is the same as the complement of the probability that a fisherman catches zero fish.

We see there are two clear paths for calculating P(1 or more fish). We can calculate P(1 fish or 2 fish or 3 fish or 4 or more fish) or we can make use of the complement and calculate1- P(0 fish). Making use of the complement requires less calculation, so we will use it here.

P(1 or more fish) = 1- P(0 fish)

We previously determined the probabilities associated with each x.