(a) There are 10 chairs in a row and 8 people to be seated. In how many ways can this be done?(b) There are 10 questions on a test and you are to do 8 of them. In how many ways can you choose them?(c) In part (a) what is the probability that the first two chairs in the row arevacant?(d) In part (b), what is the probability that you omit the first two problems in the test?(e) Explain why the answer to parts (a) and (b) are different, but the answers to(c) and (d) are the same.

Q: For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability…

A: There are 52 cards in the deck. They are divided into 4 categories and each has 13 cards, One is a…

Q: forty percent of consumers perfer to purchase electronics online.  you randoml select 8 consumers.…

A: Let X be the number of consumers who prefer to purchase electronics online. Then, for given data:…

Q: One card is drawn from a well-shuffled deck of fifty-two cards (no jokers). (a) Find the…

A: In a deck of 52 cards, there are 26 black cards and 26 red cards. a) The probability of drawing a…

Q: Both A, B, and C please

A: Given informationnumber of trials (n) = 18probability of success (p) = 45% or 0.45Required(a)…

Q: Random sample of twenty students is selected, 15% of the students are female. what is the…

A: Solution: Let X be the number of female students. From the given information, n=20 and p=0.15. Here,…

Q: You are playing a game of ring toss. There are 60 bottles set up in 6 rows of 10. You have 3 rings…

A: Let the random variable X denote the number of rings you get around the neck of the bottles. You…

Q: A gumball machine contains 6 red gumballs, 5 blue gumballs, and 4 yellow gumballs. You put a coin in…

A: Given that  A gumball machine contains Red gumballs = 6 Blue gumballs  = 5 Yellow gumballs = 4 Total…

Q: K 34% of college students say they use credit cards because of the rewards program. You randomly…

A: n=sample size=10, p=probability of college students say they use credit cards because of the rewards…

Q: You draw one card from a standard deck. (a) What is the probability of selecting a king or a queen?…

A: Given, In a well-shuffled card of 52 cards,one card is selected at random. 1) Number of kings = 4…

Q: The Video Emporium rents DVDs and Blu-rays only. They surveyed their 1,161 rental receipts for the…

A:

Q: 43​% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask…

A: Ans - Given, 43​% of adults say cashews are their favorite kind of nut. i.e  p = 0.43 You randomly…

Q: 7 total students and 20 total faculty to pick from. You want to have 10 total people on the…

A: Given data: Total number of students = 7 Total number of faculty = 20 Number of people to be…

Q: Steve has 12 biscuits in a tin. There are 5 digestive and 7 chocolate biscuits. Steve takes two…

A: Given that, Total number of biscuits = 12 5 digestive biscuits and 7 chocolate biscuits We to find…

Q: You draw one card from a standard deck. (a) What is the probability of selecting a king or queen?…

A:

Q: Suzan sees a bag of marbles; she grabs a handful at random. She has seen a bag containing 4 red…

A: 4 red marbles, 3 green ones,2 white ones,1 purple one

Q: Suzan sees a bag of marbles; she grabs a handful at random. She has seen a bag containing 4 red…

A: 4 red marbles,3 green ones,2 white ones,1 purple one.

Q: 40 percent of consumers prefer to purchase electronics online. You randomly select 8 consumers. Find…

A:

Q: You are rollling two dice and the results are added. Find Probability of: Sum not equal to 8…

A: rollling two dice  [(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4),…

Q: Max accidently mixed 56 turnip seeds with 78 cabbage seeds. Since the two seeds look nearly…

A:

Q: The chance (percentage) of having O-negative blood type is 0.06 (6%). In a class with 35 students:…

A:

Q: A gumball machine contains 6 red gumballs, 5 blue gumballs, and 4 yellow gumballs. You put a coin in…

A:

Q: There is a jar of coins sitting on the table in the center of the room. The jar contains 9 pennies,…

A: given data   jar contains : 9 - pennies    1 cent 12 - nickles  - 5 cent 10 - dimes  - 10 cent 5 -…

Q: One card is drawn from a well-shuffled deck of fifty-two cards (no jokers). (a) Find the…

A: (a) The probability formula is, Probability=Number of favourable outcomesTotal outcomes A standard…

Q: You have a box of chocolates that contains 14 pieces of which: 5 are solid chocolate, 4 are filled…

A: Given Information a box of chocolates that contains 14 pieces of which:5 are solid chocolate,4 are…

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.