Consider a pack of standard playing cards. A card is drawn at random from thepack. A card is said to be Royal if it is a Jack, Queen or King..Let A be the event that the card is a king. Let B be the event that the card is a heart.Let C be the event that the card is royal. Let D be the event that the card is black.Calculate the following probabilities.(1) P(A)(2) P(ANB)(4) P(AUC)(5) P(BD)(3) P(C)(6) P(AUD)

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Flip two fair coins. Find the probabilities of the events. a. Let F = the event of getting at most one tail (zero or one tail). b. Let G = the event of getting two faces that are the same. c. Let H = the event of getting a head on the first flip followed by a head or tail on the second flip.
In a game, if after tossing a coin the outcome is head, you have to toss it again. If the outcome is tail, then you have to throw a die. What is the probability that a die shows a number greater than 4 given that there is at least 1 tail?
A bag contains 5 red balls and 3 white balls. If 3 balls are drawn with replacement from the bag, what are the probabilities that. a. 2 balls will be red? b. a least 2 balls will be red?
Debi sells eggs at a farmer's market. She sells the eggs by the dozen, and most of the eggs are large white eggs but she also has some small brown eggs. If there is one small brown egg in every 3 dozen eggs, and Debi sells 20 dozen eggs, what is the probability that an eg chosen at random from the eggs that she sells is a sma brown egg?
Consider you are in a game of chess. You are black so your opponent is first to move. How many ways can your opponent make his first move? If all outcomes considered equally likely, what is the probability that your opponent will make an opening in a way he can move one of his bishops for the next turn?
Tom has a standard set of pool balls. If he were to draw one ball at random, what is the probability that it will be red or yellow? Give your answer in its simplest form.
Suppose that it is equally likely for a child to be a boy or a girl. Suppose a parent tells you that she or he has 6 children. What is the probability that at least one is a boy given that at least 5 of the children are girls?
Three cards are drawn from a deck without replacement. What is the probabilitythat they are not all kings?
A card is drawn at random from an ordinary deck of 52 playing cards. Find the probability that it is (a) an king of hearts, (b) a two of diamonds or a seven of spades, (c) any suit except spades, (d) a five or a spades, (g) neither a king nor a heart.
A bag contains 8 red marbles, 5 white marbles, and 6 blue marbles. You draw 3 marbles out at random, without replacement. Find the following probabilities.The probability that all the marbles are red is . (Please enter a reduced fraction) The probability that none of the marbles are red is . (Please enter a reduced fraction)
Guadalupe plays a game where she draws one card from a well-shuffled standard deck of 52 cards 2. She wins the game if the card she draws is a King or an Ace Are the two events mutually exclusive? O There is not enough information to determine if the two events are mutually exclusive. O The two events are mutually exclusive. O The two events are not mutually exclusive. What is the probability that Guadalupe wins the game? What is the probability that Guadalupe loses the game?
An executive has to visit 1 of his 5 plants for an inspection. If these plants are numbered 1, 2, 3, 4, and 5, and if he selects the plant he will visit at random, find the probability that he will do the following. (Enter your probabilities as fractions.) (a) visit plant number 3 (b) visit an odd-numbered plant (c) not visit plant number 5

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