The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that either Rebecca or Elise will be chosen to represent her school?

Q: You have three jars of gumballs. The first jar has 80 white gumballs and 20 green, the second jar…

A: Ist jar =80 white+20 green Second jar: 80 white+170 blue Third jar: 500 white+20 red

Q: Bag A contains 6 red and 7 black balls and Bag B contains 9 red and 6 black balls. One ball is…

A: Given Data : Bag A contains 6 red and 7 black balls                       Bag B contains 9 red and 6…

Q: Out of a class of 30 students, there are 16 students who study Latin, 21 who study German, and 7 who…

A: Given,no.of students who study Latin(L)=16no.of students who study German(G)=21no.of students who…

Q: A cave dweller has a choice between 3 paths. Each path has the possibility of leading to treasure.…

A: Solution

Q: You have 10 hats: 3 baseball hats, 2 cowboy hats, and the remaining are beach hats. You also have 3…

A: The objective of this question is to find the probability of choosing a beach hat and a white shirt…

Q: In an assembly of 200 people there approximately 2% of them are civil engineers. If we randomly…

A: Givenn=200p=0.02x=no.of people being civil engineersx~Binomial(n=200,p=0.02)P(X=x)=Cxn px (1-p)n-x…

Q: A gathering with 750 professionals is held. Females make up 450 of the attendees. Half of the female…

A: Given that  Total attendees=750 Female attendees=450 Male attendees=750-450=300 Female attendees…

Q: A group consists of 10 girls and 8 boys. They are to sit sit side by side on a bench. What is the…

A: Given that there are 10 girls and 8 boys. So total (10+8)=18 girls and boys. So 18 persons can be…

Q: Haroldo, Xerxes, Regina, Shaindel, Murray, and Georgia are invited to a dinner party.  They arrive…

A: Given data:   The total number of guests invited to the party is n=6.   The expression for the…

Q: A small bag of skittles has 8 red, 9 blue, and 3 green candies. A box of chocolates has 4 cherry, 10…

A:

Q: Alice has 8 pennies, 4 nickels, 2 dimes, and 6 quarters in her pocket. If one coin is drawn…

A:

Q: Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, and Georgia are invited to a dinner party. They…

A: Total number of members invited to a dinner party = 7So, the total possible number of ways of…

Q: For a family with 2 children, the sample space indicating boy (B) or girl (G) is BB, BG, GB, and GG.…

A: If the first child is a boy then there can be 2 outcomes. BB and BG Among those 2 cases only BB has…

Q: In a small town there are three competing lawn service companies, A, B, and C. Each has a certain…

A: Given, In a small town there are three competing lawn service companies, A, B, and C. Each has a…

Q: Suppose that 85% of people are voting in the election. If you pick two people at random, what is the…

A: Obtain the probability that they both are voting in the election.   The probability that they both…

Q: A group of students is surveyed and 55% of the group is from Midland and 40% of the group like…

A: According to the provided data, the probabilities are;

Q: what is the probability that George will be elected?

A: Here given, In an upcoming congressional election, two democrats, Al and Bill, seek the nomination…

Q: Use combinations to answer the following problem: I want to choose a group of students from my…

A: Combination:It represents the number of ways to choose x elements from a set of n elements. In…

Q: If Mrs. Hiatt chooses two students, what is the probability that Emily will not be one of them?

A: Mrs. Hiatt puts the names of all 15 of her second period students on popsicle sticks and places them…

Q: The athletic department of a school has 16 full time coaches, and 4 of them are female. The director…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: The dining hall is trying to decide between five different meal options to serve on Monday. We will…

A: The number of different meal options is 5.

Q: A painting is selected at random from the three Manila painters, what is the probability that it won…

A:

Q: Paul has 6 black pens, 3 red pens, and 14 pencils in his desk drawer if he reaches into his desk…

A: 6 black pens3 red pens14 pencils __________23 total itemsselect one at random. P(grab a pen) = ?

Q: In Bayside County, 45% of voters are registered Democrats. If three voters are selected at random,…

A: Given, P = 0.45 n = 3 x = 3 Here we use binomial distribution

Q: A circle of friends consist of 10 individuals. 3 of them likes chocolate, 2 likes 1 point strawberry…

A: 10 individuals such that 3 like chocolate, 2 like 1 point strawberry and 5 like vanilla The number…

Q: What is the probability that Tori picks a boy? What is the probability that Tori picks someone…

A: Here Given  Tori writes the 5 names of his Friends (Tom, Jill, Joe, Marvin, and Ginger.  ) And he…

Q: In Alex's drawer she has 11 pairs of socks, 4 of which are white, and 15 tee shirts, 2 of which are…

A: Given, Alex's has 11 pairs of socks, 4 of which are white. Alex's has 15 tee shirts, 2 of which are…

Q: A committee has seven members. There are three members that currently serve as the board's chairman,…

A:

Q: From a group of 10 choldren, a team of 5 (the red team) is randomly chosen. The remaining 5 children…

A: Given from a group of 10 children, a team of 5 children is randomly chosen. The remaining 5 children…

Q: Suppose 33.3% of high school students eat pizza and 42% drink soda. If 17.3% of high school students…

A: P(high school students of eating pizza), P(A) = 0.333 P(high school students of drink soda), P(B) =…

Q: n a certain county in Michigan, the rate of vaccinated school-aged children is 86%. If 30 children…

A: P(Vaccinated) = p = 0.86sample size : n = 30X = Number of vaccinated childrenP(x=25) = ? Number of…

Q: In a deck of 52 cards, what is the probability of getting a hand of five cards and getting exactly…

A: The number of ways to select 5 cards from deck of 52 cards=C552=52!5!…

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.