A pair of fair dice is tOssed. DeTine the events A and B as folloWs. Complete parts a through a below. A: {A 4 is rolled} (The sum of the numbers of dots on the upper faces of the two dice is equal to 4.) B: {At least one of the two dice is showing a 3} (Simplify your answers. Type integers or fractions.) Since the probability of each sample point in A n B is and there is/are sample point(s) in An B, P(A N B) = (Simplify your answers. Type integers or fractions.) Since the probability of each sample point in A UB is and there is/are sample point(s) in AU B, P(A U B) = (Simplify your answers. Type integers or fractions.) Since the probability of each sample point in A is sample point(s) in A°, P (A°) = ]. and there is/are (Simplify your answers. Type integers or fractions.) c. Use the additive rule to find P(A U B). Compare your answer with that for the same event in part b. Jse the additive rule to find P(A U B). P(A U B) = (Simplify your answer. Type an integer or a fraction.) Compare your answer for P(A U B) in part c with that for the same event in part b. The result for P(A U B) using the additive rule is the result for P(A U B) from summing the probabilities of the sample points.
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.
![A pair of fair dice is tOssed. DeTine the events A and B as folloWs. Complete parts a through a below.
A: {A 4 is rolled} (The sum of the numbers of dots on the upper faces of the two dice is equal to 4.)
B: {At least one of the two dice is showing a 3}
(Simplify your answers. Type integers or fractions.)
Since the probability of each sample point in A n B is
and there is/are
sample point(s) in An B, P(A N B) =
(Simplify your answers. Type integers or fractions.)
Since the probability of each sample point in A UB is
and there is/are
sample point(s) in AU B, P(A U B) =
(Simplify your answers. Type integers or fractions.)
Since the probability of each sample point in A is
sample point(s) in A°, P (A°) = ].
and there is/are
(Simplify your answers. Type integers or fractions.)
c. Use the additive rule to find P(A U B). Compare your answer with that for the same event in part b.
Jse the additive rule to find P(A U B).
P(A U B) =
(Simplify your answer. Type an integer or a fraction.)
Compare your answer for P(A U B) in part c with that for the same event in part b.
The result for P(A U B) using the additive rule is
the result for P(A U B) from summing the probabilities of the sample points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd210f98b-1208-4eea-a54e-043fbbd49724%2F867ac1db-e057-4817-9bcd-e9e187ab26f3%2Ftax042o.png&w=3840&q=75)
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