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Probability of Different Scenarios

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1. A study of 200 advertising firms revealed their income after taxes:

Income after Taxes Number of Firms
Under $1 million 102
$1 million to $20 million 61
$20 million or more 37

a. What is the probability an advertising firm selected at random has under $1 million in income after taxes?
b. What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? What rule of probability was applied?

2. A sample of 2,000 licensed drivers revealed the following number of speeding violations.

Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000

a. What is the experiment?
b. List one possible event.
c. What is the probability that a particular driver had exactly two speeding violations?
d. What concept of probability does this illustrate?

3. A normal population has a mean of 80.0 and a standard deviation of 14.0.

a. Compute the probability of a value between 75.0 and 90.0.
b. Compute the probability of a value 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0.

4. A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. Assume the distribution of hourly wages follows the normal probability distribution. If we select a crew member at random, what is the probability the crew member earns:

a. Between $20.50 and $24.00 per hour?
b. More than $24.00 per hour?
c. Less than $19.00 per hour?

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Solution Summary

This solution determines the probability of several factors in various scenarios.

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Probability Concept Scenarios

Please help me to check my answers to the following questions. Please show your work so that I may follow and compare against my own:

a) In how many ways can seven banquet speakers be seated along one side of the head table?

b) Gym lockers are to be numbered from 1 to 99 using individual metal number plates to be placed on each locker. How many 7's are needed?

c) In how many ways can a hostess place six name placecards around a round table?

d) In how many ways can five different keys be put in a flat leather key case?

e) In how many ways can five different keys be put on a key ring?

f) You have one apple, one orange, one banana, and one grapefruit. How many different ways can you hand out all the fruit to 5 people, if no person gets more than one kind of fruit?

g) If I am to paint our house by myself, it will take 4 days to complete painting the house. If my wife is to paint the house alone, it will take 6 days to complete her work. How many days will it take to paint our house if we decide to work together (without fight)?

h) Joey and Ross along with 4 other best friends go to see a movie. They find a row of 6 seats, but Joey and Ross don't want to sit next each other. How many different seating arrangements are possible if Joey and Ross don't want to sit next each other?
?

[2](10) At a certain gas station, 40% of all customers fill their tanks. Of those who fill their tanks, 80% pay with a credit card.
a) What is the probability that a randomly selected customer fills his or her tank and pays with a credit card?

b) If three customers are randomly selected, what is the probability that all three fill their tanks and pay with a credit card?

?
[3](10) There is a saying about initial public offerings (IPOs) of stock: "If you want it, you can't get it; if you can get it, you don't want it." This is because it is often difficult for the general public to obtain shares initially when a "hot" new company first goes on sale. Instead, most of us have to wait until it starts trading on the open market, often at a substantially higher price. Suppose that, given that you can obtain shares at the initial offering, the probability of the stock performing well is 0.35. However, given that you are unable to initially purchase shares, the probability of the stock performing well is 0.80. Overall, assume that you can obtain shares in about 15% of IPOs.
a) Find the probability that both you are able to purchase the stock at the initial offering and the stock performs well.

b) Find the probability that the stock turned out not to perform well if you were unable to obtain such shares.

c) How much access to successful IPOs do you have? That is, what is the probability that you can purchase successful IPOs?

d) What percentage of the time, over the long run, will you be pleased with the outcome?

[4](10) You are to select two cards one at a time from a well-shuffled deck of 52 playing cards (jokers not allowed). You want to get a heart as the first card and a King (K) as the second.
a) If you are given one of the following two options to do this, which option would you choose,
? Option #1: to be allowed to select the first card and put it back into the deck before selecting the second card, or
? Option #2: to be allowed to keep the first card (not to put it back to the deck) and select the second one?
Explain why you think your choice is better than the other option.

b) What is the probability to select such two cards under option #1?

c) What is the probability to select such two cards under option #2?

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