1
Tracie spins the four-colored spinner shown below. She records the total number of
times the spinner lands on the color red and constructs a graph to visualize her results.
Which of the following statements is TRUE?
If Tracie spins the spinner 1,000 times, it would land on red close to 250 times.
If Tracie spins the spinner 1,000 times, the relative frequency of it landing on red will
remain constant.
If Tracie spins the spinner 4 times, it will land on red at least once.
The theoretical probability of the spinner landing on red will change with every spin
completed.
RATIONALE
If we make the assumption that the area of the colors represents the true proportion,
then each color is equally weighted. Since there are four colors we would expect them
to come up roughly 1/4 of the time. So on 1000 rolls the expected value = n*p =
1000*0.25 = 250.
CONCEPT
Law of Large Numbers/Law of Averages
2
Two sets A and B are shown in the Venn diagram below.
, Which statement is TRUE?
There are a total of 17 elements shown in the Venn diagram.
Set A has 12 elements.
Set B has 5 elements.
Sets A and B have 15 common elements.
RATIONALE
The number of elements of Set A is everything in Circle A, or 10+2 = 12 elements.
The number of elements of Set B is everything in Circle B, or 5+2 = 7 elements, not 5
elements.
The intersection, or middle section, would show the common elements, which is 2
elements, not 15 elements.
To get the total number of items in the Venn diagram, we add up what is in A and B and
outside, which is 10+2+5+3 = 20 elements, not 17 elements.
CONCEPT
Venn Diagrams
, 3
Using the Venn Diagram below, what is the conditional
probability of event B occurring, assuming event A has happened
[P(B|A)]?
0.41
0.63
0.24
0.77
RATIONALE
To get the probability of B given A has occurred, we can use the following conditional
formula:
The probability of A and B is the intersection, or overlap, of the Venn diagram, which is
0.41.
The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65.
Tracie spins the four-colored spinner shown below. She records the total number of
times the spinner lands on the color red and constructs a graph to visualize her results.
Which of the following statements is TRUE?
If Tracie spins the spinner 1,000 times, it would land on red close to 250 times.
If Tracie spins the spinner 1,000 times, the relative frequency of it landing on red will
remain constant.
If Tracie spins the spinner 4 times, it will land on red at least once.
The theoretical probability of the spinner landing on red will change with every spin
completed.
RATIONALE
If we make the assumption that the area of the colors represents the true proportion,
then each color is equally weighted. Since there are four colors we would expect them
to come up roughly 1/4 of the time. So on 1000 rolls the expected value = n*p =
1000*0.25 = 250.
CONCEPT
Law of Large Numbers/Law of Averages
2
Two sets A and B are shown in the Venn diagram below.
, Which statement is TRUE?
There are a total of 17 elements shown in the Venn diagram.
Set A has 12 elements.
Set B has 5 elements.
Sets A and B have 15 common elements.
RATIONALE
The number of elements of Set A is everything in Circle A, or 10+2 = 12 elements.
The number of elements of Set B is everything in Circle B, or 5+2 = 7 elements, not 5
elements.
The intersection, or middle section, would show the common elements, which is 2
elements, not 15 elements.
To get the total number of items in the Venn diagram, we add up what is in A and B and
outside, which is 10+2+5+3 = 20 elements, not 17 elements.
CONCEPT
Venn Diagrams
, 3
Using the Venn Diagram below, what is the conditional
probability of event B occurring, assuming event A has happened
[P(B|A)]?
0.41
0.63
0.24
0.77
RATIONALE
To get the probability of B given A has occurred, we can use the following conditional
formula:
The probability of A and B is the intersection, or overlap, of the Venn diagram, which is
0.41.
The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65.
