a) If the probabilities that Joan, Beverly and Evelyn will be elected secretary of a ski club are 1/8, 2/5, and 1/3 respectively, find the probability that one of the three will be elected.

b) Chris and Janet are among twenty girls who enter a tennis tournament. What is the probability that either one of these two girls will win the tournament?

c) If the probabilities that Mary and Sue will receive awards in a contest are 3/5 and 1/3 respectively, what is the probability that one or the other will receive an award?

d) A bag contains six white balls, four green balls, and three brown balls. If three balls are drawn, one at a time, and the ball is replaced after each drawing, what is the probability that the balls drawn will be green, white and brown?

Assume the returns from holding small-company stocks are normally distributed. Also assume the average annual return for holding the small-company stocks for a period of time was 16.3 percent and the standard deviation of those stocks for the period was 34 percent. Use the NORMDIST function in Excel® to answer the following questions.

What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 3 decimal places, e.g., 32.161.)

Probability             %

What is the approximate probability that your money will triple in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 8 decimal places, e.g., 32.16161616.)

Probability             %

A study reports that 36% of companies in Country A have three or more female board directors. Suppose you select a random sample of 100 respondents. Complete parts​ (a) through​ (c) below.

a. What is the probability that the sample will have between 33​% and 43​% of companies in Country A that have three or more female board​ directors?

b. The probability is 70​% that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population​ percentage?

c. The probability is 99.7​% that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population​ percentage?

The probability is 99.7​% that the sample percentage will be contained above _____ ​% and below _____ ​%.

1.)the chair of the board of directors says, "there is a 50% chance this company will earn a profit, a 30% chance it will lose money next quarter." a.) use an addition rule to find the probability the company will not lose money next quarter B.) use he complement rule to find the probability it will not lose money next quarter.

2.)suoose P(X₁ )=.75 and P(Y₂|X₁)=.40. what is the joint probability of X₁ & Y₂

3.)An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value. (2) decreasing in value, or (3) remaining same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.

John knows that monthly demand for his product follows a normal distribution with a mean of 2,500 units and a standard deviation of 425 units. Given this, please provide the following answers for John.

a. What is the probability that in a given month demand is less than 3,000 units?

b. What is the probability that in a given month demand is greater than 2,200 units?

c. What is the probability that in a given month demand is between 2,200 and 3,000 units?

d. What is the probability that demand will exceed 5,000 units next month?

e. If John wants to make sure that he meets monthly demand with production output at least 95% of the time. What is the minimum he should produce each month?

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The probability that a random gift box in Overwatch (PC game) has one of the character skins you want is .1. Suppose you get a gift box every game you play, and that you play until you have obtained 2 of these skins. a. What is the probability that you play until you have x boxes that do not have the desired prize? Write down the formula as well as the notation for the pdf. b. What is the probability that you play exactly 5 times? Show the R code. c. What is the probability that you play at most 5 times? Show the R code. d. How many boxes without the desired skins do you expect to get? Show the formula

Grades on an english test can be modeled as a normal distribution with mean 80 and standard deviation 5.

A) if the english department is awarding students with test grades in the top 5%, find the lowest grade a student needs to receive the award.

B) A student is randomly selected from the class so the distribution of this student's test grade is N(80,5), what is the probability that this student scored above a 90?

C) What is the probability that the student in part b scored exactly a 90?

D) If 5 students are randomly selected from the class. what is the probability that exactly 3 of them scored above a 90?

E) If 20 students are randomly selected from the class what is the probability that at least 12 of them scored above an 80?

A person has 5 coins in his pocket. Two have both sides being heads, one has both sides being tails, and two are normal. The coins cannot be distinguished unless one looks at them.

a) The person closes his eyes, picks a coin from pocket at random, and tosses it. What is the probability that the down-side of the coin is heads?

b) He opens his eyes and sees that the up-side of the coin is heads. What is the probability that the downside is also heads (namely, this is a two-heads coin).

c) Without looking at the other side of the coin, he tosses it again. What is the probability that the downside is heads?

d) Now he looks at the upside of the coin and it is heads. What is the probability that the downside of the coin is heads?

Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and haircuts are given at a rate of 3 per hour. Assume the basic Poisson-Exponential model and answer the following questions.

1. What is the probability that the barber is idle?

2. What is the probability that one customer is getting a haircut and no one is waiting in the line?

3. What is the probability that one customer is receiving a haircut and one customer is in the line waiting?

4. What is the probability that one customer is receiving a haircut and two customers are waiting in the line.

5. On the average, how many customers are in the shop?

6. On the average, how long is the line?

7. What is the average time in the line before service begins.

8. If a customer arrives at 10:00 AM, when should he expect to leave the shop?

Using? PERT, Adam Munson was able to determine that the expected project completion time for the construction of a pleasure yacht is 22 ?months, and the project variance is 9.

?a) The probability that the project will be completed in 13 months? = nothing ?(round your response to four decimal? places).

?b) The probability that the project will be completed in 21 months? = nothing ?(round your response to four decimal? places).

?c) The probability that the project will be completed in 25 months? = nothing ?(round your response to four decimal? places).

?d) The probability that the project will be completed in 31 months? = nothing ?(round your response to four decimal? places).

?e) The due date that yields a? 95% chance of completion? = nothing months ?(round your response to two decimal? places).