Question

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

Answer #1

**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.**

1.)
Find the odds for and the odds against the event rolling a fair die
and getting a 3 or 4.
2.) Halfway through the season a soccer player has made 15
penalty kicks in 26 attempts. What is the relative frequency
probability that she will make her next penalty kick?
3.) You toss a coin 100 times and get 93 tails. what is the
relative frequency probability? Determine the expected frequency of
the event as well.
4.) Find the...

In a situation where we have a biased coin that is tails with
probability 0.7 and we independently flip it 10 times. Find the
following probabilities.
1. getting the sequence HTHHHTHTTH?
2. exactly 4 tails?
3. at least 4 tails?
4. expected number of tails? expected number of heads?

1. A fair die is tossed twice ,find the probability of
getting a 4 or 5 on the first toss and find the probability of
getting 1, 2 or 3 on the second toss?
2. Diana draws a card at random deck of cards without replacing the
card that she drawed , what is the probability that the first card
is a 3 and a second card is a diamond ?

A novelty die with six sides is printed with the numbers 1, 2,
3, 4, 8, 16. (a) If the die is rolled once what is the probability
of geting an odd number? (b) If the die is rolled twice and the
numbers for each roll added together, what is the probability of
getting an odd sum?

A die is weighted in such a way that each of 2, 4, and 6 is
three times as likely to come up as each of 1, 3, and 5. Find the
probability distribution.
Outcome
1
2
3
4
5
6
Probability
What is the probability of rolling less than 3? HINT [See
Example 3.]

Assume we roll a fair four-sided die marked with 1, 2, 3 and
4.
(a) Find the probability that the outcome 1 is first observed after
5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are
both observed.
(c) Find the expected number of rolls until the outcome 3 is
observed three times.
(d) Find the probability that the outcome 3 is observed exactly
three times in 10 rolls
given that it is first observed...

Assume we roll a fair four-sided die marked with 1, 2, 3 and
4.
(a) Find the probability that the outcome 1 is first observed after
5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are
both observed.
(c) Find the expected number of rolls until the outcome 3 is
observed three times.
(d) Find the probability that the outcome 3 is observed exactly
three times in 10 rolls
given that it is first observed...

1. A company has the choice between two different types
of dies. One cost less, but it also has a shorter life expectancy.
The expected cash flows after taxes for the two different dies are
as follows:
Die
0
1
2
3
4
A
(10,000)
8,000
8,000
B
(12,000)
5,000
5,000
5,000
5,000
The cost of money of the firm is 10%. Assume that the
selected die will be used for many years to come. Analyze the two
options and...

1. A random experiment consists of throwing a pair of dice, say
a red die and a green die, simultaneously. They are standard
6-sided dice with one to six dots on different faces. Describe the
sample space.
2. For the same experiment, let E be the event that the sum of
the numbers of spots on the two dice is an odd number. Write E as a
subset of the sample space, i.e., list the outcomes in E.
3. List...

An unfair coin is such that on any given toss, the probability
of getting heads is 0.6 and the probability of getting tails is
0.4. The coin is tossed 8 times. Let the random variable X be the
number of times heads is tossed.
1. Find P(X=5).
2. Find P(X≥3).
3. What is the expected value for this random variable?
E(X) =
4. What is the standard deviation for this random variable? (Give
your answer to 3 decimal places)
SD(X)...

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