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Chapter 4: Problem 66

Explain the meaning of the intersection of two events. Give one example.

Short Answer

Expert verified
The intersection of two events in probability represents the set of outcomes that are common to both events. For instance, if event A is 'It will rain tomorrow' and event B is 'It will be windy tomorrow', then the intersection of the two events (A 鈭� B) is 'It will rain and be windy tomorrow'.

Step by step solution

01

Understanding Events

In probability theory, an event is a set of outcomes to which a probability is assigned. It corresponds to a set of outcomes that satisfy a certain condition in a statistical experiment.
02

Interpreting Intersection of Two Events

The intersection of two events, A and B (denoted as A 鈭� B), is the event comprising all the outcomes that are common to A and B. This concept is equivalent to the logical conjunction 'and'.
03

Example

Consider the event A: 'It will rain tomorrow' and event B: 'It will be windy tomorrow'. The Intersection of these two events (A 鈭� B) represents the situation where 'It rains and is windy tomorrow'.

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Most popular questions from this chapter

Find the joint probability of \(A\) and \(B\) for the following. a. \(P(B)=.59\) and \(P(A \mid B)=.77\) b. \(P(A)=.28\) and \(P(B \mid A)=.35\)

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