4. Probability

Suppose that you roll a pair of dice 1000 times and get seven 350 times. Based on these results, what is the probability that the next roll results in seven?

A process of analyzing data to identify meaningful relations and trends is called data what?

In the context of probability and statistics, what is the main difference between a $\mathrm{parameter}$ and a $\mathrm{statistic}$?

A fair six-sided die has one blue face and five non-blue faces. What is the probability that a player will need to toss the die at least $2$ times before blue lands faceup for the first time?

87. College Football A stem-and-leaf plot for the numbers of touchdowns allowed by the 127 NCAA Division I Football Bowl Subdivision teams in the 2020-2021 season is shown. Find the probability that a team chosen at random allowed (a) at least 51 touchdowns. Are any of these events unusual? Explain. (Source: National Collegiate Athletic Association)

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The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics)

A person who earned a degree in the year is randomly selected. Find the probability that the degree earned by the person is a

a. bachelor's degree.

Gestation Period versus Weight The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.

e. What is the probability that a randomly selected baby born in 2017 weighed less than 1000 grams and was postterm? Is this event possible?

Six FlagsIn 2011, Six Flags St. Louis had 10 roller coasters: The Screamin’ Eagle, The Boss, River King Mine Train, Batman the Ride, Mr. Freeze, Ninja, Tony Hawk’s Big Spin, Evel Knievel, Xcalibur, and Sky Screamer. Of these, The Boss, The Screamin’ Eagle, and Evel Knievel are wooden coasters. Ethan wants to ride two more roller coasters before leaving the park (not the same one twice) and decides to select them by drawing names from a hat.

b. What is the probability that Ethan will ride Mr. Freeze and Evel Knievel?

Given that $X$ has a Poisson distribution with parameter $\lambda$, which of the following is the correct expression for the probability that $X$ equals $k$?

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?

For a standard normal random variable $Z$, what is the probability that $0.3<Z<3.2$?

Which of the following correctly states the two requirements for a discrete probability distribution?

Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the

probability of each event. (Source: American College Health Association)

a. Randomly selecting a student who never used marijuana

Titanic Survivors The following data represent the survival data for the ill-fated Titanic voyage by gender. The males are adult males and the females are adult females.

a. What is the probability that the passenger survived?

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.