Suppose two dice are tossed (for each die, it is equallylikely that 1, 2, 3, 4, 5, or 6 dots will show). a What is the probability that the total of the two dicewill add up to 7 or 11? b What is the probability that the total of the two dicewill add up to a number other than 2 or 12?c Are the eventsE1 first die shows a 3E2 total of the two dice is 6independent events?d Are the events 12.4 Bayes’ Rule 713E1 first die shows a 3E2 total of the two dice is 7independent events?e Given that the total of the two dice is 5, what is theprobability that the first die showed 2 dots? f Given that the first die shows 5, what is the proba-bility that the total of the two dice is even?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Suppose two dice are tossed (for each die, it is equally
likely that 1, 2, 3, 4, 5, or 6 dots will show).
a What is the probability that the total of the two dice
will add up to 7 or 11?
b What is the probability that the total of the two dice
will add up to a number other than 2 or 12?
c Are the
E1 first die shows a 3
E2 total of the two dice is 6
independent events?
d Are the events
12.4 Bayes’ Rule 713
E1 first die shows a 3
E2 total of the two dice is 7
independent events?
e Given that the total of the two dice is 5, what is the
probability that the first die showed 2 dots?
f Given that the first die shows 5, what is the proba-
bility that the total of the two dice is even?
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