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Exercises Probability and the bell curve

Example 3.2 from Statistics, 3.1 Terminology

Terminology: example 3.2

A fair, six-sided die is rolled. The sample space, S, is {1, 2, 3, 4, 5, 6}. Describe each event and calculate its probability.

Event T = the outcome is two.
Event A = the outcome is an even number.
Event B = the outcome is less than four.
The complement of A
A GIVEN B
B GIVEN A
A AND B
A OR B
A OR B′
Event N = the outcome is a prime number.
Event I = the outcome is seven.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. T = {2}, P(T) = $\frac{number of outcomes in T}{number of outcomes in S}$ = $\frac{1}{3}$
2. A = {2, 4, 6}, P(A) = $\frac{3}{6}$ = $\frac{1}{2}$
3. B = {1, 2, 3}, P(B) = $\frac{3}{6}$ = $\frac{1}{2}$
4. A′ = {1, 3, 5}, P(A′) = $\frac{3}{6}$ = $\frac{1}{2}$
5. A|B = {2}, There are three outcomes in B, and only 1 of these lies in A, so P(A|B) = $\frac{1}{3}$
6. B|A = {2}, There are three outcomes in A, and only 1 of these lies in B, so P(B|A) = $\frac{1}{3}$
7. A AND B = {2}, P(A AND B) = $\frac{1}{6}$
8. A OR B = {1, 2, 3, 4, 6}, P(A OR B) = $\frac{5}{6}$
9. A OR B′ = {2, 4, 5, 6}, P(A OR B′) = $\frac{4}{6}$ = $\frac{2}{3}$
10. N = {2, 3, 5}, P(N) = $\frac{1}{2}$
11. It is impossible to roll a die and get an outcome of 7, so P(7) = 0.

How did it go?

PreviousTerminology: example 3.1 Next Terminology: example 3.3

From Statistics (High school edition) by OpenStax (Rice University), section 3.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.