Exam 8: Probability: the Mathematics of Chance

For a casino game, you pay $4 and roll a die. The casino keeps your $4 but pays you back the number of dollars you roll. (Roll a 6 and you get $6.) Your average loss per bet is:

A license plate code consists of two letters followed by three digits. The letters cannot repeat, but the digits can. What is the probability that a randomly chosen plate has all three digits the same?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Every hour a sample of 20 bearings is drawn, measured, and the mean diameter of the sample found. What is the standard deviation _x of the sample mean?

If there is a 0.8 probability of rain today, what is the probability it will not rain?

Below is a probability model for the number of automobiles owned by a randomly chosen family in a large town. What is the mean number of automobiles owned? Number of automobiles 0 1 2 3 Probability 0.15 0.20 0.55 0.10

Suppose you use a spinner to choose a random number between 0 and 1. Which is more likely-choosing a number between 1/3 and 2/3 or between 1/2 and 3/4?

Suppose a trial consists of rolling a single die and reporting the number that is rolled. What are the possible outcomes? Are they equally likely?

Three dice are rolled and the sum of the numbers rolled is recorded. The outcomes in the sample space are all equally likely.

Two coins are flipped at the same time and heads or tails is recorded. The sample space for this is:

Suppose a game has four outcomes: A, B, C, and D. The probability of outcome A is 0.4, the probabilities of each of the other outcomes is 0.2. A player receives $2 if outcome A occurs, $3 if outcome B occurs, $1 if outcome C occurs, and must pay $5 if outcome D occurs. What is the mean value of one trial of this game?

"The probability of winning the $3 prize in your state's lottery is 1/137" means:

If you roll two dice and record their sum, the events "even" and "less than or equal to 6" are:

For a sample space {2,3,4,5,6}, two events are defined as follows: Event A: A chosen number is greater than 4 Event B: A chosen number is a prime number; that is, 2, 3, or 5 Are those events A and B dependent or independent?

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What is the probability that one potato chosen at random will weigh more than 1.65 pounds?

The shelf life of a battery produced by one major company is known to be Normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What range of years contains 68% of all battery shelf lives?

The weight of bags of potato chips produced by one machine at a packaging plant has a standard deviation of 0.3 ounces. A sample of chip bags is to be drawn and the mean weight calculated. How large must the sample be if the standard deviation of the sampling distribution is to be 0.1 ounce?

The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution of study times is Normal, what percent of students spend more than 25.238 hours per week on homework? Use the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean.

Use the following information to answer the Questions: A company gives a new screening test to test its employees for tuberculosis (TB). The results are summarized in the following table. Test result Has TB Does not have TB Positive 21 14 Negative 4 140 -If a randomly selected employee has TB, what is the probability that the employee has a positive test result?

Use the following to answer the questions: You roll two dice and record the sum shown. The sample space is the set of all possible sums, which are 2, 3, . . . , 11, 12. -The probability of the event "the sum is 5" is:

A student is taking a five-question true/false test. If the student chooses answers at random, what is the probability of getting all questions correct?