# Testing the Significance of the Correlation Coefficient

Understanding Terminology and Symbols

It is important to read each problem carefully to think about and understand what the events are. Understanding the wording is the first very important step in solving probability problems. Reread the problem several times if necessary. Clearly identify the event of interest. Determine whether there is a condition stated in the wording that would indicate that the probability is conditional; carefully identify the condition, if any.

Example

The sample space S is the whole numbers starting at one and less than 20.

a. S = _____________________________ Let event A = the even numbers and event B = numbers greater than 13.

b. A = _____________________, B = _____________________

c. P(A) = _____________, P(B) = ________________

d. A AND B = ____________________, A OR B = ________________

e. P(A AND B) = _________, P(A OR B) = _____________

f. A′ = _____________, P(A′) = _____________

C| PROBABILITY TOPICS

g. P(A) + P(A′) = ____________

h. P(A|B) = ___________, P(B|A) = _____________; are the probabilities equal?

Solution 3.1 a. S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

b. A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, B = {14, 15, 16, 17, 18, 19}

c. P(A) = , P(B) =

d. A AND B = {14,16,18}, A OR B = 2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19}

e. P(A AND B) = , P(A OR B) =

f. A′ = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19; P(A′) =

g. P(A) + P(A′) = 1 ( + = 1)

h. P(A|B) = = , P(B|A) = = , No

3.1 The sample space S is the ordered pairs of two whole numbers, the first from one to three and the second from one to four (Example: (1, 4)).

a. S = _____________________________

Let event A = the sum is even and event B = the first number is prime.

b. A = _____________________, B = _____________________

c. P(A) = _____________, P(B) = ________________

d. A AND B = ____________________, A OR B = ________________

e. P(A AND B) = _________, P(A OR B) = _____________

f. B′ = _____________, P(B′) = _____________

g. P(A) + P(A′) = ____________

h. P(A|B) = ___________, P(B|A) = _____________; are the probabilities equal?

Example

A fair, six-sided die is rolled. Describe the sample space S, identify each of the following events with a subset of S and compute its probability (an outcome is the number of dots that show up).

a. Event T = the outcome is two.

b. Event A = the outcome is an even number.

c. Event B = the outcome is less than four.

d. The complement of A.

e. A GIVEN B

f. B GIVEN A

g. A AND B

h. A OR B