Little Lotto In the Illinois Lottery game Little Lotto, an urn contains balls numbered 1–39. From this urn, 5 balls are chosen randomly, without replacement. For a \$1 bet, a player chooses one set of five numbers. To win, all five numbers must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning Little Lotto with one ticket?

In Problems 7–16, determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.  

Three cards are selected from a standard 52-card deck without replacement. The number of aces selected is recorded.

Acceptance Sampling Suppose that you have just received a shipment of 100 televisions. Although you don’t know this, 6 are defective. To determine whether you will accept the shipment, you randomly select 5 televisions and test them. If all 5 televisions work, you accept the shipment; otherwise, the shipment is rejected. What is the probability of accepting the shipment?

[NW] Selecting a Jury

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.

c. What is the probability of selecting a jury of two students and three faculty?

In Problems 7–16, determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.  

A basketball player who makes 80% of her free throws is asked to shoot free throws until she misses. The number of free-throw attempts is recorded.

In Problems 7–16, determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.  

One hundred randomly selected U.S. parents with at least one child under the age of 18 are surveyed and asked if they have ever spanked their child. The number of parents who have spanked their child is recorded.

If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution. If a population has A objects of one type (such as lottery numbers you selected), while the remaining B objects are of the other type (such as lottery numbers you didn’t select), and if n objects are sampled without replacement (such as six drawn lottery numbers), then the probability of getting x objects of type A and objects of type B is

In New Jersey’s Pick 6 lottery game, a bettor selects six numbers from 1 to 49 (without repetition), and a winning six-number combination is later randomly selected. Find the probability of getting exactly four winning numbers with one ticket.

A school is holding a fair raffle and a teacher is interested in predicting how many winners will be from her class. Determine which probability distribution she should use given the following information.

(A) There are 386 tickets, one for each student. Tickets are placed back in the pool after being chosen and 5 tickets are drawn.