A set of 6 cards contains two black cards numbered 1 and 2 and four red cards numbered 1, 2, 3, 4. Each of the questions below refers to uniformly selecting one card from the set of 6. i What is the probability that you draw a card whose value is 4? 1 ii What is the probability that you draw a card whose value is 4 given the card is black? iii What is the probability that you draw a card whose value is 4 given the card is red?

Q: In a football match, suppose that the probability of Team A winning is 0.3, Team B winning is 0.5…

A: #let x be the nonof match end with tie with probability p=0.2 follow binomial distribution…

Q: A deck consists of playing cards that can have one of 12 suits and one of 6 ranks. A hand is a set…

A: It is required to find the number of possible four of a kind hands from the deck, and the…

Q: A bag contains 4 white and 6 black balls.  If 2 balls are drawn in succession without replacement,…

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Q: Suppose that the probability of having a boy or a girl is 50%. Answer the following questions: What…

A: Calculation: It is given that the probability of having a boy or a girl is 50%. Thus, the…

Q: One student is to be selected at random from a group of 7 freshmen, 5 sophomores, 8 juniors, and 3…

A: 7 freshmen, 5 sophomores, 8 juniors, and 3 seniors  Total=23

Q: A drum contains 4 black balls, 5 red balls and 6 green balls. If 5 balls are selected at random,…

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Q: What is the probability of getting a head when tossing a coin? A school has 820 male students and…

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Q: George has two red socks and two white socks in a drawer. What is the probability of picking a red…

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Q: A new superman Mastercard has been issued to 2000 customers. Of these customers, 1500 hold a Visa…

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Q: During a game of Blackjack, three players are dealt two cards each, and the dealer has two cards. No…

A: The probability shows how likely an event occurs and its value lies between 0 and 1.

Q: From 10 cards bearing the letters a, b, c, d, e, f, g, h, i and j a card is drawn. Find the…

A: Among a, b, c, d, e, f, g, h, i, and j, the vowels are a, e, i. So there are 3 vowels. There are 10…

Q: Suppose that 22% of people have a dog, 15% of people have a cat, and 2% of people own both. What is…

A: Given that, 22% of people have a dog15% of people have a cat2% of people own both

Q: As shown above, a classic deck of cards is made up of 52 cards, 4 suits with clubs and spades black…

A: From the provided information, Total cards = 52 Total cards of 5 number = 4 Total cards of 8 number…

Q: Given a deck of cards of cards.  Choose five cards without replacement.  Determine the probability…

A: In a given deck of 52 cards, the objective is to find the probability that of the obtained 5 cards…

Q: My friends owns 21 tapes. I want to help her randomly arrange 10 of them in a tape rack. What is the…

A: Given data my friend owns 21 tapes. I want to help her randomly by arranging 10 of them in tape…

Q: Suppose you have 10 drinks, 6 regular and 4 diet, in a cooler. You select two at random. Answer the…

A: Given that there are 10 drinks in a cooler. Which are 6 regular and 4 diet, two drinks selected at…

Q: You choose a letter at random from the alphabet. What is the probability that it will be the letter…

A: Given : we have given letter n, g, l, a, s  No. of letters = 5 No. of  alphabet = 26 One letter is…

Q: Three piggy banks each contain 20 coins: • Piggy Bank # 1 contains 12 gold coins, 5 silver coins and…

A: Probability : Probability is a field of mathematics that deals with numerical descriptions of how…

Q: 90​% of Dr.​ William's patients end up with​ 20-30 vision or better. Find the probability that…

A: Given data,n=7P=90%=0.90P(x=6)=?

Q: Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. If she chooses two of these…

A: Let A be the 10-cent coin and B be the 25-cent coin. Number of coins worth 10 cents = 5 Number of…

Q: Ali has taken two books with him for holiday. The probability of liking the first book is 0.5, the…

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Q: The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each…

A: Given problem Given that The chess clubs of two schools consist of, respectively 8 and 9 players.…

Q: Eli has a jar full of marbles. In the jar there are 1818 blue​ marbles, 1010 red marbles and 1111…

A: Step 1: Given informationNumber of blue marbles = 1818Number of red marbles = 1010Number of purple…

Q: Your friend throws two dice and tells you that one of the dice is a 4. What is the probability that…

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Q: 1. Suppose that two runners from team A and three runners from team B participate in a race. Further…

A: General formula of probability ,  Probability = Number of favorable outcomes Total outcomes…

Q: n a group of 100 students, 80 study Physics, 90 study Math and 5 study none of the subjects. What…

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Q: A game is player with a pair of tetrahedral ( four sided) dice. Each die has four faces numbered…

A: if a pair 4 sided die is rolled than the possible outcomes…

Q: re 1 dx dy. x(1+ y²) Compute the value of the series n=1 n+1

A: To find the value of given series first we solve the integration.          ∑n=1∞…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.