Question 2

Scenario: A statistical software consultant requests assistance for various packages. The packages include SPSS, SAS, Minitab, JMP, and R.

Events:

  • - Next request for help is for the SPSS package.
  • - Next request for help is for the SAS package.

Probabilities:

  • .
  • .

(a)

Question: Why is it not the case that ?

Process: would only be true if and are the only two events which partition the sample space. Since there are other types of requests which can be made aside from these two, then the sum of their probabilities can't be 1.

Answer: The probabilities do not add to 1 because there are other software packages for which requests could be made.

(b)

Question: Calculate .

Process: The probability of the complement of is the probability of minus 1.

Answer: 0.90.

Summary

The probability of the complement of an event is:

(c)

Question: Calculate .

Process: Since and are mutually exclusive, the probability of the union between them is the probability of and added together.

Answer: 0.60.

Summary

The probability of the union of and if they're mutually exclusive is:

(d)

Problem: Calculate .

Process: According to De Morgan's laws, we can rewrite as . So, we're really trying to find the probability of the complement of the union of and . As noted earlier, we find the probability of the complement of set by subtracting the probability of the set from 1.

Answer: 0.40.

Summary

For the probability of a selected object belonging to neither nor , see the Question 1 (c) Summary.