Question

# 1) At a lumber company, shelves are sold inȱȱ5 types of wood, 4 different widths and...

1) At a lumber company, shelves are sold inȱȱ5 types of wood, 4 different widths and 3 different lengths. How many different types of shelves could be ordered?

2) A shirt company has 5 designs each of which can be made with short or long sleeves. There are 4 different colors available. How many differentȱȱshirts are available from this company? Find the indicated probability. Round your answer to 2 decimal places when necessary.

3) A bag contains 6 red marbles, 4 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary.

4) Of 1428 people who came into a blood bank to give blood, 328 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. Find the indicated probability. Round your answer to 2 decimal places when necessary.

5) What is the probability of not rolling aȱȱnumber larger than 5 with a fair die?

6) If a person is randomly selected, find the probability that his or her birthday is not in May. ignore leap years.

Make a probability distribution for the given set of events.

7) When four fair coins are tossed, sixteen equally likely outcomes are possible as shown below:HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Make a probability distribution for the number of tails when four fair coins are tossed.

A) Result Probability 0 T 1/16 1 T 1/8 2 T 3/8 3 T 1/8 4 T 1/16 B) Result Probability 0 T 1/16 1 T 1/4 2 T 3/8 3 T 1/4 4 T 1/16 C) Result Probability 1 T 1/4 2 T 7/16 3 T 1/4 4 T 1/16 D) Result Probability 0 T 1/16 1 T 3/16 2 T 1/2 3 T 3/16 4 T 1/16

Find the indicated probability.

8) A die is rolled 50 times with the following results. Outcome 1 2 ȱȱ3 ȱȱ4 ȱȱ5 6 Frequency ȱȱ7 4 11 23 2 3

Compute the empirical probability that the die comes up a 5.

9) A die is rolled 100 times with the following results. Outcomeȱ ȱȱ1 2 3 4 5 6 Frequency 14 20 24 21 9 12

Compute the empirical probability that the die comes up 2 or 3. 10) Sean flipped a coin 100 times and got heads 42 times.

He concludes that the probability of getting heads on a flip of his coin is 0.42. Which method did Sean use?

A) Theoretical method B) Multiplication method C) Empirical method D) Subjective method

Provide an appropriate response.

11) Given that P(E) = 1, what must be true about the event E?

A) The event E is possible but not likely. B) The event E is certain. C) The event E is probable but not certain. D) The event E is impossible.

12) Which of the following could not possibly be probabilities? A.ȱȱ C.ȱȱ0 B.ȱȱ 13 7 D.ȱȱ0.43 Find the expected value.

13) Numbers is a game where you bet \$2.00 on any three -digit number from 000 to 999. If your number comes up, you get \$500.00. If your number doesnȇt come up, you lose your \$2. Find the expected net winnings. Solve the problem.

14) Suppose a charitable organization decides to raise money by raffling a trip worth \$500. If 5,000 tickets are sold at \$1.00 each, find the expected net winnings for a person who buys 1 ticket. Find the expected value.

15) A commercial building contractorȱȱis trying to decide which of two projects to commit her company to. Project A will yield a profit of \$50,000 with a probability of 0.6, a profit of \$80,000 with a probability of 0.3, and a profit of \$10,000 with a probability of 0.1. Project B will yield a profit of \$100,000 with a probability of 0.1, a profit of \$63,000 with a probability of 0.7, and a loss of \$20,000 with a probability of 0.2. Find the expected profit for each project. Based on expected values, which project should the contractor choose? A) Project A: \$46,000 Project B:ȱȱ\$50,100 Contractor should choose project B B) Project A:\$55,000 Project B:ȱȱ\$50,100 Contractor should choose project A C) Project A: \$46,666 Project B:ȱȱ\$47,666 Contractor should choose project A D) Project A: \$55,000 Project B:ȱȱ\$58,100 Contractor should choose project B Provide an appropriate response.

16) A fair coin is tossed 5 times. Which of the following statements is (are) true? A: The sequence HTHTH is more likely than the sequence HHHHH. B:ȱȱThe sequence HTHTH and the sequence HHHHH are equally likely. C: Getting 5 tails is less likely than getting 3 tails. D: Getting 5 tails and getting 3 tails are equally likely. A) A and C B) B and D C) A and D D) B and C

17) An insurance company sells an insurance policy for \$1000. If there is no claim on a policy, the company makes a profit of \$1000. If there is a claim on a policy, theȱȱcompany faces a large loss onȱȱthat policy. The expected value to the company, per policy, is \$250. Which of the following statements is (are) true? A: The most likely outcome on any single policy is a profit for the company of \$250. B: If the company sells only a few policies, its profit is hard to predict. C: If the company sells a large number of policies, the average profit per policy will be close to \$250. A) B only B) A and C C) B and C D) C only

Solution:

Question 1)

We are given that: At a lumber company, shelves are sold in 5 types of wood, 4 different widths and 3 different lengths.

We have to order a shelve.

Since to order a shelve ,we must select one kind of wood from given 5 types of wood , one kind of width from 4 different widths and one kind of length from 3 different lengths, we use multiplication principle of counting

Thus total number of ways in which a shelve can be ordered = 5 X 4 X 3 = 60 ways.

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