Find the solutions

Q.1 . An insurance company writes policies for a large number of newly-licensed

drivers each year. Suppose 40% of these are low-risk drivers, 40% are

moderate risk, and 20% are high risk. The company has no way to know which

group any individual driver falls in when it writes the policies. None of the

low-risk drivers will have an at-fault accident in the next year, but 10% of the

moderate-risk and 20% of the high-risk drivers will have such an accident. If a

driver has an at-fault accident in the next year, what is the probability that he or

she is high-risk?

25. You are to participate in an exam for which you had no chance to study, and for

that reason cannot do nothing but guess for each question (all questions being

of the multiple choice type, so the chance of guessing the correct answer for

each question is 1/d, d being the number of options (distractors) per question;

220so in case of a 4-choice question, your guess chance is 0.25). Your instructor

offers you the opportunity to choose amongst the following exam formats: I. 6

questions of the 4-choice type; you pass when 5 or more answers are correct;

II. 5 questions of the 5-choice type; you pass when 4 or more answers are

correct; III. 4 questions of the 10-choice type; you pass when 3 or more

answers are correct. Rank the three exam formats according to their

attractiveness. It should be clear that the format with the highest probability to

pass is the most attractive format. Which would you choose and why?

26. Consider the question of whether the home team wins more than half of its

games in the National Basketball Association. Suppose that you study a simple

random sample of 80 professional basketball games and find that 52 of them

are won by the home team.

a. Assuming that there is no home court advantage and that the home team

therefore wins 50% of its games in the long run, determine the probability that

the home team would win 65% or more of its games in a simple random

sample of 80 games.

b. Does the sample information (that 52 of a random sample of 80 games are

won by the home team) provide strong evidence that the home team wins more

than half of its games in the long run? Explain.

27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11

plums, and 2 mangos.

a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit

at random. What is the probability that you will pull out a pear?

b. Imagine now that you put your hand in the refrigerator and pull out a piece

of fruit. You decide you do not want to eat that fruit so you put it back into the

refrigerator and pull out another piece of fruit. What is the probability that the

first piece of fruit you pull out is a banana and the second piece you pull out is

an apple?

c. What is the probability that you stick your hand in the refrigerator one time

and pull out a mango or an orange

A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow

marble. Two marbles are chosen (without replacement). (a) What is the

probability that one will be green and the other red? (b) What is the probability

that one will be blue and the other yellow?

10. You roll a fair die five times, and you get a 6 each time. What is the probability

that you get a 6 on the next roll?

11. You win a game if you roll a die and get a 2 or a 5. You play this game 60

times.

a. What is the probability that you win between 5 and 10 times (inclusive)?

b. What is the probability that you will win the game at least 15 times?

c. What is the probability that you will win the game at least 40 times?

d. What is the most likely number of wins.

e. What is the probability of obtaining the number of wins in d?

Explain how you got each answer or show your work.

12. In a baseball game, Tommy gets a hit 30% of the time when facing this pitcher.

Joey gets a hit 25% of the time. They are both coming up to bat this inning.

a. What is the probability that Joey or Tommy will get a hit?

b. What is the probability that neither player gets a hit?

c. What is the probability that they both get a hit?

13. An unfair coin has a probability of coming up heads of 0.65. The coin is flipped

50 times. What is the probability it will come up heads 25 or fewer times?

(Give answer to at least 3 decimal places).

14.You draw two cards from a deck, what is the probability that:

a. both of them are face cards (king, queen, or jack)?

b. you draw two cards from a deck and both of them are hearts?

2. The mean mathematics SAT score in 2015 was 514 with a standard deviation of 11?. Assume the mathematics SAT score is normally distributed. Also draw the normal curves wherever necessary.r a.) State the random variable. (2 Marks) to Find the probability that a person has a mathematics SAT score over 700 (6 Marks) c.) Find the probability that a person has a mathematics SAT score of less than 400. (6 Marks) a; Find the probability that a person has a mathematics SAT score between a 5'30 and a 650 (6 Marks) of 4 Sheet 2 Question (1) In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the probability that (a) the student take mathematics or history; (b) the student take history but not mathematics; (c) the student does not take history if he took mathematics. Solution:Consider the following information about job opportunities for new college graduates in Megalopolis: Table 5_1 Major Probability of Receiving an Offer In One Year Average Salary Offer Accounting 0.95 $25,000 Economics 0.90 $30,000 English 0.70524,000 Poli Sci 0.60 $18,000 Mathematics 1.00 $21,000 Refer to Table 5.1. Expected income for the first year is A. higher in English than in mathematics. B. higher in political science than in economics. C. highest in mathematics. D. highest in economics. E. highest in accounting. Consider the following information about job opportunities for new college graduates in Megalopolis: Table 5.1 Major Probability of Receiving an Offer In One Year Average Salary Offer Accounting 0.95 $25,000 Economics 0.90 930,000 English 0.70 $24,000 Poli Sci 0.60 $18,000 Mathematics 1.00 $21,000 Refer to Table 5.1. Expected income for the first year is A. higher in English than in mathematics. B. higher in political science than in economics. C. highest in mathematics. D. highest in economics. E. highest in accounting-7 Exercise 7 In a certain college, 25% of the students failed mathematics, 15% failed chemistry and 10% failed both mathematics and chemistry. A student is selected at random. a) Dene the two relevant events. b) If the student failed chemistry, what is the probability that he failed mathematics? (3) If the student failed mathematics, what is the probability that he failed chemistry? (1) What is the probability that the student failed mathematics or chemistry e) What is the probability that the student failed neither mathematics nor chemistry