4. Probability

5. Which event(s) in Exercise 4 can be considered unusual? Explain your reasoning.

Which of the following is classified as ordinal-level data?

Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of \$1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect \$500, so your net profit is \$499.

a. Find the actual odds against winning.

Flipping a Coin What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.

In Exercises 21-28, find the probability and answer the questions.

Genetics: Eye Color Each of two parents has the genotype brown/blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. (The actual determination of eye color is more complicated than that.)

b. What is the probability that a child of these parents will have the blue/blue genotype?

Statistical methods are most effective for analyzing which type of data?

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

Using Probabilities for Significant Events

d. Is 1 a significantly low number of matches? Why or why not?

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)?

[DATA] A Random Process: Trains Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow. So, getting stopped by a train will likely make you late for work. You start recording data to determine the likelihood of arriving at the tracks while a train is there. Open data set 5_1_37 at www.pearsonhighered.com/sullivanstats, which contains the day number and whether a train was present, or not, for 200 consecutive days in which you drove to work. The column “Train” shows a series of 0s and 1s. In that column, a 0 indicates there was no train present and a 1 indicates that a train was present. The column “Aggregate Train” represents the cumulative number of times a train was present. The column “Aggregate Proportion Train” represents the cumulative proportion of times a train was present.

d. Were you stopped by a train on the 30th day?

b. Would an empirical probability based on 100 games or 1000 games give a better estimate of the probability of winning Solitaire? Why?

Explain what is meant by a subjective probability. List some examples of subjective probabilities.

Who Do You Trust?

According to the National Constitution Center, 18% of Americans trust organized religion.

c. In a random sample of three Americans, all three indicated they trust organized religion. Is this result surprising?

In Pennsylvania’s Cash 5 lottery, balls are numbered 1 to 43. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability of winning Pennsylvania’s Cash 5 with one ticket.

[NW] Verify that the following is a probability model. What do we call the outcome “blue”?