McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. Probabilities of Mutually Exclusive Events
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Exercise 32 Page 930

Two events that cannot happen at the same time are said to be mutually exclusive.

Not mutually exclusive, see solution.

Practice makes perfect

We are asked whether the events of choosing a complex number and choosing a natural number are mutually exclusive. First, let's recall the definition of mutually exclusive events.

Two events that cannot happen at the same time are said to be mutually exclusive.

Now, let's suppose that we are choosing from the following numbers.

Recall that natural numbers form a subset of complex numbers. Notice that the first number 1+0* i is a complex number and also a natural number because 1+0* i=1, which is a natural number. Therefore, if we choose the first number we will choose a complex number and a natural number.

This means that the events of choosing a complex number and choosing a natural number can happen at the same time. Thus, the events are not mutually exclusive.