Сollege level probability practice problems, solved and explained

Recent questions in Upper level probability

Makatu Zuma 2022-05-03

200.54

2022-05-01

Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?

2022-04-28

Sally has caught covid but doesn’t know it yet. She is testing herself with rapid antigen kits which have an 80% probability of returning a positive result for an infected person. For the purpose of this question you can assume that the results of repeated tests are independent.
a) If sally uses 3 test kits what is the probability that at least one will return a positive result?
b) In 3 tests, what is the expected number of positive results?
c) Sally has gotten her hands on more effective tests, these ones have a 90% probability of returning a positive result for an infected person. If she tested herself
twice with the new tests, how many positive results would she expect to see?

2022-04-28

Sally has caught covid but doesn’t know it yet. She is testing herself with rapid antigen kits which have an 80% probability of returning a positive result for an infected person. For the purpose of this question you can assume that the results of repeated tests are independent.
a) If sally uses 3 test kits what is the probability that at least one will return a positive result?
b) In 3 tests, what is the expected number of positive results?
c) Sally has gotten her hands on more effective tests, these ones have a 90% probability of returning a positive result for an infected person. If she tested herself
twice with the new tests, how many positive results would she expect to see?

2022-04-28

Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?

2022-04-24

Consider an electric refrigerator located in a room. Determine the direction of the work and heat interactions (in or out) when the following are taken as the system:
(a) the contents of the refrigerator,
(b) all parts of the refrigerator including the contents, and
(c) everything contained within the room during a winter day.

2022-04-14

A large cooler contains the following drinks: 6 lemonade, 8 Sprite, 15 Coke, and 7 root beer. You randomly pick two cans, one at a time (without replacement).
(a) What is the probability that you get 2 cans of Sprite?
(b) What is the probability that you do not get 2 cans of Coke?
(c) What is the probability that you get either 2 root beer or 2 lemonade?
(d) What is the probability that you get one can of Coke and one can of Sprite?
(e) What is the probability that you get two drinks of the same type?

Jesenmanuefan 2022-04-04

Carrillo Valdivia Brian Jafet 2022-04-04

(1 point) A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood. The device is not totally reliable: 7 % of drivers who have not consumed an excess of alcohol give a reading from the breathalyser as being above the legal limit, while 10 % of drivers who are above the legal limit will give a reading below that level. Suppose that in fact 14 % of drivers are above the legal alcohol limit, and the police stop a driver at random. Give answers to the following to four decimal places.

Part a)
What is the probability that the driver is incorrectly classified as being over the limit?

Part b)
What is the probability that the driver is correctly classified as being over the limit?

Part c)
Find the probability that the driver gives a breathalyser test reading that is over the limit.

Part d)
Find the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit.

2022-04-02 Answered

help me answer the question 5.9 a

2022-04-01 Answered

Assume that the monthly worldwide average number of airplaine crashes of commercial airlines is 2.2 $2.2$ . What is the probability that there will be) at most 2 $2$ such accidents in the next 2 $2$ months?

jamilla.ricag093004 2022-03-31

A wallet containing five 100-peso bills, four 200-peso bills, one 500-peso bill, and seven 1,000-peso bills. Which of the following probability distribution table is the appropriate to describe the given situation? *

2022-03-30

individual plays a game of tossing a coin where he wins Rs 2 if head turns up and nothing if tail turns up.On the basis of the given information, find (i) The expected value of the game. (4) (ii) The risk premium this person will be willing to pay to avoid the risk associated with the game.

desireegarvin 2022-03-22

Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 5 adult smartphone users are randomly selected, find the probability that at least 3 of them use their smartphones in meetings or classes.

2022-03-22

2022-02-04 Answered

Binomial Distribution. We conduct 8 trials with a probability π=.63 of success.

Alan Smith 2022-01-14 Answered

What is Var(X - Y)?
We know that the formula for Var(X + Y) is Var(X) + Var(Y) + 2Cov(X,Y)
Does this mean that for Var(X - Y) it is just:
Var(X) - Var(Y) - 2Cov(X,Y)?

2021-12-20 Answered

In fall 2014, 34% of applicants with a Math SAT of 700 or more were admitted by a certain university, while 16% with a Math SAT of less than 700 were admitted. Further, 36% of all applicants had a Math SAT score of 700 or more. What percentage of admitted applicants had a Math SAT of 700 or more? (Round your answer to the nearest percentage point.)

Daniell Phillips 2021-12-19 Answered

Evenats A and B are mutually exclusive. Which of the following statements is also true?
a. $P (A \cap B) = P (A) + P (B)$
b. $P (A \cup B) = P (A) + P (B)$
c. A and B are also independent
d. $P (A \cup B) = P (A) P (B)$

Yulia 2021-08-11 Answered

An analysis of variance of the yields of five different varieties of wheat, observed on one plot each at each of six different locations. The data from this randomized block design are listed here:
Varieties, Location 1, Location 2, Location 3, Location 4, Location 5, Location 6
A, 35.3, 31.0, 32.7, 36.8, 37.2, 33.1
B, 30.7, 32.2, 31.4, 31.7, 35.0, 32.7
C, 38.2, 33.4, 33.6, 37.1, 37.3, 38.2
D, 34.9, 36.1, 35.2, 38.3, 40.2, 36.0
E, 32.4, 28.9, 29.2, 30.7, 33.9, 32.1
a. Use the appropriate nonparametric test to determine whether the data provide sufficient evidence to indicate a difference in the yields for the five different varieties of wheat. Test using αα=.05.
b. How do the analysis of variance F test compare with the test in part a? Explain.

The majority of college-level probability practice problems will include questions related to statistics with the answers and explanations that will explain how a certain riddle has been addressed. Just think about flipping a coin or throwing dice as an example or finding a red marble in the bag with the green marbles. It is all about probability where the college probability will have more complex questions with the necessity of different equations and quantitative data questions where formulas must be used to determine the possibility of a certain outcome or prognosis. We offer help by letting you see various probability examples.

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