An experiment consists of casting a pair of fair six sided dice (one green and one red) and observing the number that fallsuppermost on each die.a) Find the sample space for this experiment.b) Determine the event, E, that the sum of the numbers falling uppermost is greater than 9.c) Determine the event, F, that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die isgreater than 5.d) Are the events E and F mutually exclusive?e) Find the event, G, that a 5 is rolled or the sum of the dice is at least 10.
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.
An experiment consists of casting a pair of fair six sided dice (one green and one red) and observing the number that falls
uppermost on each die.
a) Find the
b) Determine the
c) Determine the event, F, that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die is
greater than 5.
d) Are the events E and F mutually exclusive?
e) Find the event, G, that a 5 is rolled or the sum of the dice is at least 10.
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