A standard deck of cards consists of 52 cards of 13 types (2,3,...,10,J,Q,K and ace) and 4 colors (hearts, spades, diamonds and clubs), and each combination of type and color appears exactly once. We simultaneously draw 4 cards in random from a standard deck of 52 cards.   What is the probability that we drew exactly 2 aces and exactly 2 hearts?

Q: A pet store has 11 puppies, including 4 poodles, 5 terriers, and 2 retrievers. If Rebecka and Aaron,…

A: No.of poodles=4 No.of terriers=5 No.of retrievers=2 Total puppies=11

Q: A box contains 12 chocolates: 5 dark chocolates, 4 milk chocolates, and 3 white chocolates. If two…

A:

Q: 10 animals are randomly put into a line. There are 3 cats and 4 dogs. What is the probability all…

A: Solution

Q: A committee of two people needs to be chosen. There are two men and six women available to serve on…

A:

Q: The mathematics faculty at a certain college consists of 10 full professors, 6 associate professors,…

A: From the given information, thee are  10 full professors 6 associate professors 12 assistant…

Q: A bag contains 10 red marbles, 6 blue marbles, and 4 green marbles. If three marbles are drawn…

A: 10 red marbles 6 blue marbles 4 green marbles ____________________ 20 total marbles   select 3…

Q: A company has 12 salespeople and 18 engineers. If a committee of 4 is randomly selected, what is the…

A: given data, 12- salespeople18- engineers30- total persona commitee of 4 is randomly…

Q: you have 20 jelly beans in a jar: 2 yellow, 3 blue, 4 green, 5 red, 6 orange jelly beans (a) if you…

A: There are 20 jelly beans in a jar: 2 yellow, 3 blue, 4 green , 5 red and 6 orange jelly beans. First…

Q: The first box contains 3 black and 6 white cards. The second box contains 4 black and 3 white cards.…

A: It is given that there are 3 black and 6 white cards in box 1 and 4 black and 3 white cards in box…

Q: A subcommittee is to be selected from a committee of men and women. For this problem, assume that…

A:

Q: This problem involves inspection at a widget factory. Assume that a box contains 2 defective widgets…

A: Answer:- Given that a box contains 2 defective widgets and 15 acceptable widgets.  So, Probability…

Q: A class consists of 10 male and 30 female students. Of the 30 females, only 5 did not have pet. Six…

A: The probability of an event E  is defined as the ratio of favourable number of outcomes to the total…

Q: In a large bag of marbles, there are 20 red, 15 blue, and 10 green marbles. If three marbles are…

A: From the provided information, In a large bag of marbles, there are 20 red, 15 blue, and 10 green…

Q: Dolly is randomly selecting a new duo of alpaca to pull her wagon.  There are 5 black alpaca, 7 tan…

A: Probability of an event = Number of event divided by total possible outcomes = n/s

Q: I pick the 5 of hearts from a deck of cards.  If the 5 of hearts is not returned to the deck, what…

A: There are four 5s and 13 hearts in a deck of cards After drawing the 5 of hearts there will be…

Q: A club at CBC has 6 History Majors, 5 English Majors, and 8 Psychology Majors. If a committee of 3…

A: It is given that there are 6 History, 5 English, and 8 Psychology Majors. Thus, Consider that n is…

Q: Pat randomly chooses marbles from an urn with replacement. The urn originally contained 55 red​…

A:

Q: A class consists of 10 males and 30 females. If one student is randomly selected from the class,…

A: We have given the  that  10 males  30 females  Total = 40

Q: A small bag of M and Ms contains 7 green, 4 yellow, 5 blue, and 6 brown. If we randomly select a 1st…

A:

Q: Suppose we select 5 cards from an ordinary deck of playing cards. What is the probability of…

A: Step 1: Calculate the probability of drawing 4 diamonds and 1 club with replacement.When drawing…

Q: There are 20 red, 20 blue, and 10 yellow marbles in a bag. What is the probability of drawing two…

A: Given: Number of red marbles = 20 Number of blue marbles = 20 Number of yellow marbles = 10 Total…

Q: ) A bridge hand is made up of 13 cards from a deck of 52. Find the probability of a hand with 6 of…

A: select 13 cards from 52 card deck.  P(six cards of one suit,4 of another suit and 3 of another suit)…

Q: class consists of 50 women and 21 men. If a student is randomly selected, what is the probability…

A: According to the given information in this question, we need to find the following probability

Q: Assume that a flower bed contains 40 flowers. Suppose that 8 of the flowers are white, 8 of the…

A: Introduction: If r distinct items are to be chosen from n items without replacement so that the…

Q: Suppose you have three bowls, X, Y , and Z with some number of red and blue balls. Bowl X has 2 red…

A:

Q: In a bag of 10 marbles, 4 are red and 6 are blue. If two marbles are randomly drawn without…

A:

Q: As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color…

A: Given,Total no.of cards=52no.of cards smaller than 9 =32

Q: standard deck of 52 cards has 4 suits (Each has 13 cards: Ace, 2, 3,..., 10, Jack, Queen, and King):…

A: Given that ; A standard deck of 52 cards has 4 suits (Each has 13 cards: Ace, 2, 3,..., 10, Jack,…

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.