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Chapter 4: Problem 69

When is the following addition rule used to find the probability of the union of two events \(A\) and \(B\) ? $$ P(A \text { or } B)=P(A)+P(B) $$ Give one example where you might use this formula.

Short Answer

Expert verified
The rule \(P(A \text { or } B) = P(A) + P(B)\) is used when events A and B are mutually exclusive. An example could be the probability of drawing a heart or diamond card from a deck, as these two events can't both happen simultaneously.

Step by step solution

01

Understand mutual exclusivity

Firstly, identify the concept of mutually exclusive events. These are events that cannot happen simultaneously. In other words, if one event happens, the other cannot.
02

Recognize the applicability of the rule

The next step is to understand that the addition rule \(P(A \text { or } B) = P(A) + P(B)\) is applied when the events, A and B, are mutually exclusive. This means, the rule is used when the intersection of A and B equals zero, or in probability notation, when \(P(A \cap B) = 0\).
03

Provide an example

Now, let's consider an example: Suppose we want to find the probability of drawing a heart or a diamond from a deck of playing cards. Since these two events are mutually exclusive (a card cannot be both a heart and a diamond at the same time), the probability is simply the sum of the separate probabilities. This is a situation where the formula \(P(A \text { or } B) = P(A) + P(B)\) could be used.

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