4. Probability

Which of the following statements about conditional and marginal probabilities is correct? Select the single correct option.

In the context of $Probability$ and $Statistics$, why is a $sample$ used more often than a $population$ when conducting studies?

Which of the following statements best describes the addition rule of probability?

In Problems 39–42, use the given table, which lists six possible assignments of probabilities for tossing a coin twice, to answer the following questions.

Which of the assignments of probabilities should be used if tails is twice as likely to occur as heads?

[DATA] Walt Disney Stock The table shows the movement of Walt Disney stock for 30 randomly selected trading days. “Up” means the stock price increased in value for the day. “Down” means the stock price decreased in value for the day, and “No Change” means the stock price closed at the same price it closed for the previous day.

a. Construct a probability model for stock movement of Walt Disney stock.

Which of the following describes the probability distribution with possible outcomes $0$, $1$, and $2$, and corresponding probabilities $\frac{1}{4}$, $\frac{1}{2}$, and $\frac{1}{4}$?

The lengths of time it takes for new light bulbs to burn out are an example of which type of data?

Using a Bar Graph to Find Probabilities In Exercises 75-78, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is

77. a master's degree.

2. Determine whether each number could represent the probability of an event. Explain your reasoning. a. 25/25

Arizona’s Pick 5 In one of Arizona’s lotteries, balls are numbered 1–35. 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 Arizona’s Pick 5 with one ticket.

Suppose a continuous random variable $X$ has a uniform distribution on the interval $[2,8]$. What is the probability that $X$ will assume a value between $3$ and $5$? (Round your answer to 4 decimals.)

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 3 or more matches.

In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

8. The probability of randomly selecting five cards of the same suit from a standard deck of 52 playing cards is about 0.002.

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.