Consider the sample space and the event given below. An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards. Write the following event as a set. The event that the chosen card is red and has an even number on it. a.) E = {2♥, 4♥, 6♥, 8♥, 10♥, 2◆, 4◆, 6◆, 8◆, 10◆} b.) E = {2♥, 4♥, 6♥, 8♥, 2◆, 4◆, 6◆, 8◆} c.) E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣} d.)E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♥, 4♥, 6♥, 8♥, 10♥} e.) E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣, 2♥, 4♥, 6♥, 8♥, 10♥, 2◆, 4◆, 6◆, 8◆, 10◆} Compute its probability. Consider the sample space and the event given below. An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards. Write the following event as a set. The event that the denomination of the chosen card is at most 4 (counting aces as 14). a.) E = {A♠, 2♠, 3♠, 4♠, A◆, 2◆, 3◆, 4◆, A♣, 2♣, 3♣, 4♣, A♥, 2♥, 3♥, 4♥} b.) E = {2♠, 3♠, 2◆, 3◆, 2♣, 3♣, 2♥, 3♥} c.) E = {2♠, 3♠, 4♠, 2◆, 3◆, 4◆, 2♣, 3♣, 4♣, 2♥, 3♥, 4♥} d.) E = {A♠, 2♠, 3♠, A◆, 2◆, 3◆, A♣, 2♣, 3♣, A♥, 2♥, 3♥} e.) E = {4♠, 4◆, 4♣, 4♥} Compute its probability. Consider the sample space given below. A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each is recorded. The possible outcomes of the sample space S are listed as follows, wherein each case the die on the left is blue and the one on the right is gray. S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.) The event that the numbers showing face up are the same. E = ....................? Compute the probability of E.
Consider the sample space and the event given below. An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards. Write the following event as a set. The event that the chosen card is red and has an even number on it. a.) E = {2♥, 4♥, 6♥, 8♥, 10♥, 2◆, 4◆, 6◆, 8◆, 10◆} b.) E = {2♥, 4♥, 6♥, 8♥, 2◆, 4◆, 6◆, 8◆} c.) E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣} d.)E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♥, 4♥, 6♥, 8♥, 10♥} e.) E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣, 2♥, 4♥, 6♥, 8♥, 10♥, 2◆, 4◆, 6◆, 8◆, 10◆} Compute its probability. Consider the sample space and the event given below. An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards. Write the following event as a set. The event that the denomination of the chosen card is at most 4 (counting aces as 14). a.) E = {A♠, 2♠, 3♠, 4♠, A◆, 2◆, 3◆, 4◆, A♣, 2♣, 3♣, 4♣, A♥, 2♥, 3♥, 4♥} b.) E = {2♠, 3♠, 2◆, 3◆, 2♣, 3♣, 2♥, 3♥} c.) E = {2♠, 3♠, 4♠, 2◆, 3◆, 4◆, 2♣, 3♣, 4♣, 2♥, 3♥, 4♥} d.) E = {A♠, 2♠, 3♠, A◆, 2◆, 3◆, A♣, 2♣, 3♣, A♥, 2♥, 3♥} e.) E = {4♠, 4◆, 4♣, 4♥} Compute its probability. Consider the sample space given below. A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each is recorded. The possible outcomes of the sample space S are listed as follows, wherein each case the die on the left is blue and the one on the right is gray. S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.) The event that the numbers showing face up are the same. E = ....................? Compute the probability of E.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 24CT: Show the sample space of the experiment: toss a fair coin three times.
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Concept explainers
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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Question
Consider the sample space and the event given below.
An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards.
Write the following event as a set.
The event that the chosen card is red and has an even number on it.
a.) E = {2♥, 4♥, 6♥, 8♥, 10♥, 2◆, 4◆, 6◆, 8◆, 10◆}
b.) E = {2♥, 4♥, 6♥, 8♥, 2◆, 4◆, 6◆, 8◆}
c.) E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣}
d.)E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♥, 4♥, 6♥, 8♥, 10♥}
e.) E = {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣, 2♥, 4♥, 6♥, 8♥, 10♥, 2◆, 4◆, 6◆, 8◆, 10◆}
Compute its probability.
Consider the sample space and the event given below.
An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards.
Write the following event as a set.
The event that the denomination of the chosen card is at most 4 (counting aces as 14).
a.) E = {A♠, 2♠, 3♠, 4♠, A◆, 2◆, 3◆, 4◆, A♣, 2♣, 3♣, 4♣, A♥, 2♥, 3♥, 4♥}
b.) E = {2♠, 3♠, 2◆, 3◆, 2♣, 3♣, 2♥, 3♥}
c.) E = {2♠, 3♠, 4♠, 2◆, 3◆, 4◆, 2♣, 3♣, 4♣, 2♥, 3♥, 4♥}
d.) E = {A♠, 2♠, 3♠, A◆, 2◆, 3◆, A♣, 2♣, 3♣, A♥, 2♥, 3♥}
e.) E = {4♠, 4◆, 4♣, 4♥}
Compute its probability.
Consider the sample space given below.
A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each is recorded. The possible outcomes of the sample space S are listed as follows, wherein each case the die on the left is blue and the one on the right is gray.
| S | = | {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, |
| 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} |
Write the following event as a set. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.)
The event that the numbers showing face up are the same.
E = ....................?
Compute the probability of E.
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