Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).



Using Probabilities for Significant Events


a. Find the probability of getting exactly 2 matches.

Federal Criminal Defendants The following graph depicts results from a study of defendants in federal crime cases (based on data from the Administrative Office of the U.S. Courts).

a. If a defendant is randomly selected what is the probability that this person had their case dismissed before going to trial?

Federal Criminal Defendants The following graph depicts results from a study of defendants in federal crime cases (based on data from the Administrative Office of the U.S. Courts).

d. If three defendants are randomly selected, what is the probability that they all pleaded guilty?

Notation For a polygraph (lie detector) used when a subject is presented with a question, let L= the subject lied and let Y = the polygraph indicated that the subject told a lie. Use your own words to translate the notation P (Y|L) into a verbal statement.

Significant For 100 births, P(exactly 56 girls) and P(56 or more girls) Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

b. Find the probability of getting 2 or more matches.

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

a. Find the probability of getting exactly 3 matches.

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?

Using Probabilities for Significant Events

a. Find the probability of getting exactly 1 match.