Exam 8: Probability: the Mathematics of Chance

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. -What is the complement of the event "the sum is less than 6 or greater than 7"?

The annual income of residents in a certain county is Normally distributed, with a mean of $42,000 and a standard deviation of $10,000. What is the probability that a randomly chosen resident has income over $52,000?

Exactly one of Terry, Chris, and Kim will attend a party. The probability Terry attends is 0.31 and the probability Chris attends is 0.5. What is the probability that Kim attends?

To function correctly, each of two parts of a circuit must work. If an event denotes that the circuit functions correctly, what is the complement of the event?

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 fraction of the potatoes in the shipment will weigh between 0.25 and 2.35 pounds?

A pair of dice is rolled. Sam says there are 36 outcomes in the sample space for this procedure and Sally says there are 11 outcomes in the sample space. Explain how they could both be correct.

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. -Are the 11 outcomes equally likely?

The length of students' college careers at Anytown University is known to be Normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years. What is the lower quartile for the length of students' careers at Anytown University? Use the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean.

Suppose a password must consist of two letters followed by three digits. Repeated characters are allowed. How many such passwords are possible?

There are seven blue and six black socks in a drawer. One is pulled out at random. Find the probability that it is black.

Use the following information to solve the Questions: A random number generator is modeled by a uniform probability model with a density curve that has height 1/10 between 0 and 10 and height 0 everywhere else. -For this model, what is $P ( 0 \leq X \leq 10 ) ?$

A pizza can be made with any of the following toppings: cheese, pepperoni, sausage, mushrooms, anchovies, green peppers, or olives. How many different three-topping pizzas can be made? Doubling of any topping is not allowed.

Use the following information to solve the Questions: A random number generator is modeled by a uniform probability model with a density curve that has height 1/10 between 0 and 10 and height 0 everywhere else. -For this model, what is $P ( X < 2 \text { or } X > 7 ) ?$

The weight of bags of potato chips produced by one machine at a packaging plant has a standard deviation of 0.2 ounces. Suppose samples of 25 bags are drawn from a production run and weighed. What is the standard deviation _x of the mean result?

We need to create code words that use three letters of the alphabet. Repeating of letters is allowed. How many code words can be created?

A football stadium snack bar conducted a survey and found that 30 customers bought one item, 52 customers bought two items, 21 customers bought three items, and 12 customers bought four items. What is the mean number of items purchased per customer? Round your answer to the nearest tenth.

Three dice are tossed. The sum of the numbers rolled is recorded. How many outcomes are in the sample space?

A fair coin is tossed three times. Find the probability of getting exactly two heads.

A fair die is rolled. If a number 1 or 2 appears, you will receive $5. If any other number appears, you will pay $2. What is the mean value of one trial of this game?

If the probability that Kerry gets an A in English class is 0.82, what is the probability that Kerry does not get an A?