If 8 different books are arranged at random on a shelf, what is the probability that a certain pair of books (a) will be beside each other? (b) will not be together?

Q: Six persons are to be seated in a row. What is the probability that two particular persons sit next…

A: Given: Six persons are seated in a row.

Q: The pool of students in a calculus class consist of 22 sophomore and 8 freshmen. If seven students…

A: Let the students of sophomore year be denoted by S and freshmen be denoted by F.   Given: Number of…

Q: What is the probability that a five-card hand will contain exactly two 2's? What is the probability…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: ten?What is the probability that the number of spades in your hand and in your partner’s hand totals…

A: Here consider person and his partner consider as single entity who got 26 cards as here Required…

Q: For people are sitting around a table with two brothers.  How many different positions can they…

A: Given data four people are sitting around a table with two brothers

Q: What is the probability of four hearts in a row from a standard deck when the drawn card is returned…

A: We have to find the probability of four hearts in a row from a standard deck when the drawn card is…

Q: A family was randomly chosen from a set of families having 5 children. What is the probability that…

A:

Q: What is the probability that no two boys are sitting together for a photograph if there are 5 girls…

A:

Q: Five fishermen are chosen at random. What is the probability that at least two of them were born on…

A:

Q: What is the probability of N people in a room to have at least four people having the same birthday?

A: The probability of at least N people having same birthday can be calculated as:…

Q: When 5 digits( between 0 and 9) are randomly selected with replacement for a lottery ticket, what is…

A:

Q: An after-school club sonsists of 10 juniors and 12 seniors. If 2 students are chosen at random to…

A:

Q: Find the probability of drawing 4 aces at random from a deck of 52 ordinary cards if the cards are…

A: here total cards in deck = 52

Q: A team of 6 students from a pool of 10 students is being formed. Assume the students have different…

A: Formula : Binomial distribution is given by

Q: cards are chosen at random from a deck without replacement, what is the probability that at least…

A: We know that  There are 52 card in the deck in which they divided into two color i.e red(26) and…

Q: What is the probability of two people chosen at random being born on the same day of the week

A: Here we need to find out the probability of two people chosen at random being born on the same day…

Q: A box contains 4red and 2 blue marbles. Find the probability that if two marbles are drawn at random…

A: Given data A box contains 4 red and 2 blue marbles.

Q: if you randomly choose one bean, do NOT replace it, and randomly choose another, what is the…

A: Given: 20 jelly beans in a jar: 2 yellow, 3 blue, 4 green, 5 red, 6 orange  Without Replacement we…

Q: In a bag full of 10 marbles, 5 are yellow, 3 are blue and 2 are green. An individual picks two from…

A: A bag full of 10 marbles of which 5 are yellow, 3 are blue and 2 are green.It is given that the…

Q: If two letters are taken at random from the word HOME, what is the probability that none of the…

A:

Q: If two cards are drawn at random from a pack of cards, what is the probability that one of them is…

A: The number of cards in a deck are 52.

Q: A couple decided to have 5 children. (a) What is the probability that they will have at least one…

A:

Q: What is the probability that a hand of 4 cards contains exactly 3 cards that are the same suit?

A: We have to find given probability ...

Q: A commission of 3 people out of 5 women and 4 men working in a workplace will be formed. Which of…

A: To find the probability following rules will be used  :  Fundamental Principle of Multiplication :…

Q: What is the probability that any card picked at random from a standard deck of 52 will be a club?

A:

Q: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are…

A: no.of black cards=26no.of queen cards=4no.of balck queen cards=2Total no.of cards=52…

Q: One person has bought 10 of a total of 1000 tickets in a lottery. There are 5 different prizes that…

A:

Q: A committee of 2 is chosen at random from a population of 4 men and 5 women. What is the probability…

A: given data, A committee of 2 is chosen at random from a population4 men5 women9-total members the…

Q: What  is the probability that a hand of 5 cards chosen at random from a standard deck of 52 cards…

A: The 5 cards chosen need to have an odd number of cards from each of the four suits. There are 4…

Q: A closet contains 10 pairs of shoes. If 8 shoes are selected randomly, what is the probability that…

A: Given that, a closet contains 10 pairs of shoes mean there are 20 shoes in closet. The possible…

Q: A group of families that have 3 kids are in a group. What family that has three girls, given the…

A: Topic = Probability

Q: There are 400 seniors in highschool, of which 180 are males. It is known that 85% of the males and…

A: Given,

Q: If 10 people choose, at random, a letter from the English alphabet of 26 letters, what is the…

A: We find the probability that each of the 10 people chooses a different letter from the English…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.