(a) What is the probability that it will take four or more rolls of the dice until we get our first 4? Please compute your answer to four decimal places. (b) Suppose that it takes 5 rolls to obtain your first 4. What is the probability that the first dice was selected?
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 there are two six-sided dice such that the
resulting in a 4 is 0.2 and the probability on any roll of the second dice resulting in a 4 is 0.4.One of these dice are selected and is continually rolled until a 4 appears (at which point the
experiment stops). Assume there is a 0.3 probability the first dice is selected and that the rolls
of the dice are independent of each other.
(a) What is the probability that it will take four or more rolls of the dice until we
get our first 4? Please compute your answer to four decimal places.
(b) Suppose that it takes 5 rolls to obtain your first 4. What is the probability
that the first dice was selected? Please compute your answer to four decimal places.
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