Exam 8: Introduction to Probability

Suppose that an employer plans to hire eight people from a group of fourteen equally qualified people, of whom four are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that exactly one minority candidate is hired? Round your answer to four decimal places. ​

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9? ​

A bag contains 8 white balls and 3 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that exactly one white W ball is drawn. ​

Suppose an ice cream store offers 36 flavors of ice cream cones in sizes small, medium, and large. How many different selections of cones are possible if each cone has one flavor? ​

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S)? ​

A red ball and 19 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting a red R ball on the first draw and a white W ball on the second? ​

Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places. ​

A bag contains 7 white, 9 black, and 10 green balls. What is the probability that a ball drawn at random from the bag is white W or green G? ​

In how many ways can a committee consisting of 3 men and 7 women be selected from a group consisting of 20 men and 17 women? ​

A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially, the probabilities that a customer patronizes A, B, or C are 0.4, 0.4, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect. ​ ​ ​ If A runs the advertising campaign for 3 weeks, find the probability that a customer will still patronize business B. ​

A small town has 6500 adult males and 5000 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? ​

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn. ​

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red? ​

One ball is drawn at random from a bag containing 17 red R balls and 2 white W balls. What is the probability that the ball is red? ​

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​

A frustrated store manager is asked to make seven different yes-no decisions that have no relation to each other. Because he is impatient to leave work, he flips a coin for each decision. If the correct decision in each case was no, what is the probability that all of his decisions were correct? ​

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time? ​

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? ​

A self-administered pregnancy test detects 80% of those who are pregnant but does not detect pregnancy in 20%. It is 92% accurate in indicating women who are not pregnant but indicates 8% of this group as being pregnant. Suppose it is known that 2% of the women in a neighborhood are pregnant. If a woman is chosen at random from those living in this neighborhood, and if the test indicates she is pregnant, what is the probability, rounded to four decimal places, that she really is? ​

Suppose a box contains 2 defective transistors and 12 good transistors. If 2 transistors are drawn from the box without replacement, what is the probability that the first transistor is good G and the second transistor is defective D? ​