Use the given information to find the indicated probability. A, B, and C are mutually exc

Name: Problem 36, Chapter 7: Finite Mathematics and Applied Calculus
Uploaded: 2021-09-08T08:41:55-08:00
Duration: 1 min 14 s
Channel: Mahendra Kumar
Description: Use the given information to find the indicated probability. A, B, and C are mutually exclusive. P(A)=.2, P(B)=.6 P(C)=.1 . Find P(A ∪B ∪C).

step 1 In this question we are given with some probabilities that is probability of a is 0 .2 and proba

Question

Use the given information to find the indicated probability. $$ \begin{aligned} &A, B, \text { and } C \text { are mutually exclusive. } P(A)=.2, P(B)=.6\\ &P(C)=.1 . \text { Find } P(A \cup B \cup C). \end{aligned} $$

   Use the given information to find the indicated probability.
$$
\begin{aligned}
&A, B, \text { and } C \text { are mutually exclusive. } P(A)=.2, P(B)=.6\\
&P(C)=.1 . \text { Find } P(A \cup B \cup C).
\end{aligned}
$$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 7th Edition

Chapter 7, Problem 36

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Solved by Expert Mahendra Kumar

09/08/2021

Step 1

This means that these events cannot occur at the same time. In terms of probability, this means that the intersection of these events is empty, i.e., they have no common outcomes. Show more…

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Use the given information to find the indicated probability. $$ \begin{aligned} &A, B, \text { and } C \text { are mutually exclusive. } P(A)=.2, P(B)=.6\\ &P(C)=.1 . \text { Find } P(A \cup B \cup C). \end{aligned} $$

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Key Concepts

Mutually Exclusive Events

Mutually exclusive events are those that cannot occur at the same time. When events are mutually exclusive, the occurrence of one event precludes the occurrence of any other event in the same sample space.

Addition Rule for Probabilities

The addition rule in probability states that the probability of the union of two or more events is the sum of the probabilities of the events, minus any overlap. When the events are mutually exclusive, there is no overlap, and the probability of the union simply equals the sum of the probabilities of the individual events.

Probability of a Union of Events

The probability of a union of events refers to the likelihood that at least one of several events will occur. In cases where the events are mutually exclusive, calculating this probability involves directly adding the probabilities of each event.

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