Chapter 8 Quiz

In a Venn diagram representing two sets A and B, if the area representing A is 30% and the area representing B is 20%, what is the maximum possible area of the intersection of A and B?

• 10%

• 20%

• 25%

• 15%

Answer explanation

The maximum area of the intersection of sets A and B cannot exceed the area of the smaller set. Since B is 20%, the maximum intersection is 20%, making it the correct answer.

You are choosing what to wear and have 3 shirts (gray, red, green), 2 pairs of pants (blue or brown), and 2 pairs of shoes (black or white).

Draw a tree diagram showing all the possible combinations of shirts, pants, and shoes. How many possible outfits can you make?

Using set notation, express the union of sets A and B if A = {1, 2, 3} and B = {3, 4, 5}.

• A - B = {1, 2}

• A ∪ B = {1, 2, 3, 4, 5}

• A ∩ B = {3}

• A ∪ B = {1, 2, 3, 4}

Answer explanation

The union of sets A and B, denoted A ∪ B, combines all unique elements from both sets. Here, A = {1, 2, 3} and B = {3, 4, 5}, so A ∪ B = {1, 2, 3, 4, 5}. Thus, the correct choice is A ∪ B = {1, 2, 3, 4, 5}.

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.5, what is the probability of either A or B occurring if A and B are mutually exclusive?

• 0.7

• 0.6

• 0.9

• 0.8

Answer explanation

Since A and B are mutually exclusive, the probability of either A or B occurring is the sum of their probabilities: P(A or B) = P(A) + P(B) = 0.4 + 0.5 = 0.9. Thus, the correct answer is 0.9.

A Venn diagram shows two overlapping circles representing sets X and Y. If the area of X is 50% and the area of Y is 30%, and the intersection is 10%, what is the probability of selecting an element from either X or Y?

• 0.5

• 0.8

• 0.7

• 0.6

Answer explanation

To find the probability of selecting an element from either X or Y, use the formula: P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y). Here, P(X) = 0.5, P(Y) = 0.3, and P(X ∩ Y) = 0.1. Thus, P(X ∪ Y) = 0.5 + 0.3 - 0.1 = 0.7.

Using Bayes' theorem, if P(Disease) = 0.01, P(Positive|Disease) = 0.9, and P(Positive|No Disease) = 0.05, what is P(Disease|Positive)?

• 0.05

• 0.25

• 0.75

• 0.1538

Answer explanation

Using Bayes' theorem: P(Disease|Positive) = (P(Positive|Disease) * P(Disease)) / P(Positive). First, calculate P(Positive) = P(Positive|Disease) * P(Disease) + P(Positive|No Disease) * P(No Disease). Then substitute values to find P(Disease|Positive) = 0.1538.

In a survey, 70% of people like coffee, 50% like tea, and 30% like both. What is the probability that a randomly selected person likes either coffee or tea?

• 0.5

• 0.9

• 0.8

• 0.7

Answer explanation

To find the probability of liking either coffee or tea, use the formula: P(C ∪ T) = P(C) + P(T) - P(C ∩ T). Here, P(C) = 0.7, P(T) = 0.5, and P(C ∩ T) = 0.3. Thus, P(C ∪ T) = 0.7 + 0.5 - 0.3 = 0.9.

If two events A and B are independent, and P(A) = 0.4, what is P(A ∩ B) if P(B) = 0.5?

• 0.2

• 0.4

• 0.3

• 0.1

Answer explanation

For independent events A and B, P(A ∩ B) = P(A) * P(B). Here, P(A) = 0.4 and P(B) = 0.5. Thus, P(A ∩ B) = 0.4 * 0.5 = 0.2. Therefore, the correct answer is 0.2.

A box contains 3 red and 2 blue balls. If one ball is drawn at random, what is the probability that it is red given that it is not blue?

• 0.5

• 3

• 1

• 2

Answer explanation

There are 3 red and 2 blue balls. If we know the ball is not blue, we only consider the 3 red balls. Thus, the probability of drawing a red ball is 3 out of 3, which equals 1. Therefore, the correct answer is 1.

Draw the intersection between set A and set B: