4. Probability

Which sampling method involves dividing the population into groups ($\mathrm{strata}$) and then taking a random sample from each group?

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

Lingo

In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers that match the numbers still on the team's Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses its second draw. To form a Lingo, the team needs five numbers in a row—vertically, horizontally, or diagonally. Consider the sample Lingo board below for a team that has just guessed a mystery word.

a. What is the probability that the first ball selected is on the Lingo board?

In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.

3. Experiment: Choosing a month of the year

Event: Choosing a month that begins with the letter J

Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.

71. What is the probability that all three children are girls?

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?

In the context of estimating a population parameter, how does decreasing the confidence level affect the sample size required to achieve a fixed margin of error?

In a discrete probability distribution, the sum of all the probabilities must be equal to which of the following values?

Given the following table provides a probability distribution for the random variable $X$:

The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children.

d. Among the females, what is the probability the individual believes the ideal number of children is 2?

Which of the following events has a theoretical probability equal to $\frac{1}{3}$?

In the context of basic probability concepts, does sampling error increase as the sample size $n$ increases?

In a study, the data you collect is the number of traffic tickets each person has received. What is the level of measurement for this variable?

97. Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum.

a. List all of the possible sums and determine the probability of rolling each sum.

b. Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling

each sum.

c. Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.

Define each of the following.

e. Equally likely outcomes