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Outcomes of Variables

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1. The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities associated with each of the six possible outcome pairs are given in the accompanying two-way table.

Low Medium High
On .50 .10 .05
Off .25 .07 .03

Consider the following events:
A: {On}
B: {Medium or On}
C: {Off and Low}
D: {High}

a. Find P(A)
b. Find P(B)
c. Find P(C)
d. Find P(D.
e. Find P(A^c)
f. Find P(A or B)
g. Find P(A and C)
h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.

2. Refer to the previous exercise. Use the same event definitions to do the following exercises.
a. Write the even that the outcome is "On" and "High" as an intersection of two events.
b. Write the event that the outcome is "Low" or "Medium" as the complement of an event.

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Solution Preview

a. P(A) = 0.50 + 0.10 + 0.05 = 0.65
b. P(B) = 0.50 + 0.10 + 0.05 + 0.07 = 0.72
c. P(C) = 0.25
d. P(D) = 0.05 +0.03 = 0.08
e. P(A^c) = 1 - P(A) = 1 - 0.65 = 0.35
f. P(A or B) = P(B) = 0.72
g. P(A and C) = 0 ...

Solution Summary

Outcomes of variables are examined in probability. Six possible outcome pairs in accompanying two-way tables are determined.