A survey was carried out to find if students in the theater department liked the following three actors: Marlon Brando, Clint Eastwood and Paul Newman. Exactly 51 students participated in the survey. 26 students liked Marlon Brando. 34 students liked Clint Eastwood. 29 students liked Paul Newman. 2 students liked Paul Newman and Marlon Brando, but not Clint Eastwood. 9 students liked Paul Newman and Clint Eastwood, but not Marlon Brando. 19 students liked exactly two of the following three actors: Marlon Brando, Clint Eastwood and Paul Newman. 11 students liked all of the following three actors: Marlon Brando, Clint Eastwood and Paul Newman. a.) How many students liked exactly one of the following three actors: Marlon Brando, Clint Eastwood and Paul Newman? b.) How many students liked none the following three actors: Marlon Brando, Clint Eastwood and Paul Newman? c.) How many students liked at most two of the following three actors: Marlon Brando, Clint Eastwood and Paul Newman?
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.
A survey was carried out to find if students in the theater department liked the following
three actors: Marlon Brando, Clint Eastwood and Paul Newman. Exactly 51 students
participated in the survey.
26 students liked Marlon Brando.
34 students liked Clint Eastwood.
29 students liked Paul Newman.
2 students liked Paul Newman and Marlon Brando, but not Clint Eastwood.
9 students liked Paul Newman and Clint Eastwood, but not Marlon Brando.
19 students liked exactly two of the following three actors: Marlon Brando, Clint
Eastwood and Paul Newman.
11 students liked all of the following three actors: Marlon Brando, Clint Eastwood
and Paul Newman.
a.) How many students liked exactly one of the following three actors: Marlon Brando,
Clint Eastwood and Paul Newman?
b.) How many students liked none the following three actors: Marlon Brando, Clint
Eastwood and Paul Newman?
c.) How many students liked at most two of the following three actors: Marlon
Brando, Clint Eastwood and Paul Newman?
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