Exam 8: Introduction to Probability

A car dealer has 15 different cars that he would like to display, but he has room to display only 3. Suppose 11 of the cars are the same color, with the remaining 4 having different colors that are distinct from each other. If the dealer tells a salesperson to display any 3 cars, what is the probability that all 3 cars will be the same color? ​

A computer store offers used computers free to local middle schools. Of the 55 machines available, 15 have defective memories, 12 have defective keys, and the remainder have no defects. If a teacher picks one at random, what is the probability that she will select a defective computer? ​

A small town has 8000 adult males and 6500 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from the town. What is the probability, rounded to four decimal places, that the person is male M, if it is known that the person drinks heavily DH? ​

A small town has 5000 adult males and 7000 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from the town. What is the probability, rounded to four decimal places, that the person is male M or drinks heavily DH? ​

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R. ​

Use the transition matrix and initial probability vector to find the resulting third probability vector. Round all numerical values in your answer to three decimal places. ​

Suppose a box contains 6 defective transistors and 13 good transistors. If 2 transistors are drawn from the box without replacement, what is the probability that one of the transistors drawn is good G and one of them is defective D? ​

Suppose an ice cream store offers 34 flavors of ice cream cones in sizes small, medium, and large. If four toppings are available to put on a cone, and a cone can be bought without a topping, how many different selections of ice cream are available if each cone has one flavor and one or no toppings? ​

A ball is drawn from a bag containing 16 red balls numbered 1-16 and 12 white balls numbered 17-28. What is the probability that the ball is white W and odd-numbered O? ​

Five candidates for manager of a department store are ranked according to the weighted average of several criteria. How many different rankings are possible for the top four candidates if no two candidates receive the same rank? ​

Suppose a government study estimated that the probability of successive generations of a rural family remaining in a rural area was 0.4 and the probability of successive generations of an urban family remaining in an urban area was 0.6. Assuming a Markov chain applies to these facts, find the steady-state vector. ​

As a reward for a record year, the Ace Software Company is randomly selecting 5 people from its 70 employees for a free trip to Hawaii, but it will not pay for a traveling companion. If John and Jill are married and both are employees, what is the probability that they will both win? Round your answer to five decimal places. ​

A bag contains 6 red balls numbered 1-6 and 14 white balls numbered 7-20. If a ball is drawn, what is the probability that the ball is red R or even-numbered E? ​

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was male or black (non-Hispanic). ​ ​

What is the probability of being dealt a poker hand of 5 cards containing exactly 4 spades? Round your answer to two decimal places. ​

Suppose a box contains 7 defective transistors and 16 good transistors. If 2 transistors are drawn from the box without replacement, what is the probability that the first transistor is defective D and the second one is good G? ​

An urn contains 8 red, 9 white, and 2 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that at least one ball drawn is black B. ​

If the odds that a particular horse will win a race are 15 : 9, what is the probability that the horse will win the race? ​

The local community-service funding organization in a certain county has classified the population into those who did not give the previous year, those who gave less than their "fair share," and those who met or exceeded their "fair share." Suppose the organization developed the following transition matrix for these groups. Find the steady-state vector for this county's contribution habits. ​ ​

According to a recent medical study, 196 of 200 mammograms turn out to be normal. What is the probability that the mammogram of a woman chosen at random will show an abnormality? ​