Roll two fair dice. Each die has six faces. • Let A be the event that either a 3 or 4 is rolled first, followed by an even number. • Let B be the event that the sum of the two rolls is at most 7. O Part (a) List the sample space. (Select all that apply.) (5, 3) O(1, 2) (4, 4) (2, 4) O(5, 5) O(0, 3) O(0, 1) (0, 6) (1, 3) (5, 6) (6, 5) O(3, 1) O(4, 5) (0, 5) O(4, 6) O(3, 5) (6, 1) O(5, 2) O(0, 4) O(2, 3) O(3, 2) (5, 1) O(6, 6) O(1, 5) O(6, 2) O(3, 3) O(6, 3) O(3, 7) O(5, 7) (3, 6) O(4, 7) (2, 7) O(0, 2) (2, 2) O(1, 1) C(6, 4) O(2, 6) (2, 5) O(6, 7) O(4, 2) (3, 4) O(1, 4) O(1, 7) O(4, 1) O(2, 1) O(1, 6) O(5, 4) O(4, 3) O Part (b) Find P(A). (Enter your answer as a fraction.) P(A) = O Part (c) Find P(B). (Enter your answer as a fraction.) P(B) = O Part (d) In words, explain what "P(A | B)" represents. P(A | B) represents the probability of rolling a 3 or 4 on the first die, given that the second die is an even number. P(A | B) represents the probability that the sum of the dice is at most 7, given that the first die is a 3 or 4 and the second die is an even number. P(A | B) represents the probability of rolling a 3 or 4 on the first die, followed by an even number, given that the sum of the dice is at most 7. P(A | B) represents the probability the sum of the dice is at most 7, given that the second die is an even number. Find P(A | B). (Enter your answer as a fraction.) PLA | B)
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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Wed Feb 10 8:58 PM
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In words, explain what "P(A| B)" represents.
P(A | B) represents the probability of rolling a 3 or 4 on the first die, given that the second die is an even number.
P(A | B) represents the probability that the sum of the dice is at most 7, given that the first die is a 3 or 4 and the second die is an even number.
P(A | B) represents the probability of rolling a 3 or 4 on the first die, followed by an even number, given that the sum of the dice is at most 7.
P(A | B) represents the probability the sum of the dice is at most 7, given that the second die is an even number.
Find P(A | B). (Enter your answer as a fraction.)
P(A | B) =
Part (e)
Are A and B mutually exclusive events? Explain your answer.
The events are not mutually exclusive. Rolling 3, 2 is an outcome in event A and also an outcome in event B.
The events are not mutually exclusive. Rolling 4, 6 is an outcome in event A but not in event B.
The events are mutually exclusive. Rolling 4, 6 is an outcome in event A but not in event B.
The events are mutually exclusive. Rolling 3, 2 is an outcome in event A and also an outcome in event B.
Part (f)
Are A and B independent events? Explain your answer.
Events A and B are dependent because they have outcomes in common.
Events A and B are dependent because the probability of event A happening is affected by whether event B has happened.
Events A and B are independent because they are mutually exclusive.
Events A and B are independent because the roll of one die has no effect on the outcome of rolling a second die.
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• Let P(C) = 0.2
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a)
Two dice are thrown.
Sample space is given as follows:
Select the options as shown above.
Ignore the options which contains 0 or 7.
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