Q: A die is rolled. Let $$A be $$the event 'even number' and $$B be$$ 'number less than or equal to 4'. Are $$A$$ and $$B$$ independent?

No, because $$P(A \cap B) \neq P(A) \cdot P(B)$$

Question 1

A business experiment involves flipping two coins and recording the outcome. What is the probability of getting at least one tail?

Accepted Answer

$$\frac{3}{4}$$

Question 2

Given the sample space $$S = \{HH, HT, TH, TT\}$$ for flipping two coins, which of the following is a compound event?

Accepted Answer

$$\{HT, TH\}$$

Question 3

A company randomly selects two smartphones from an assembly line. The probability table is shown. What is the probability that exactly one is defective?

Accepted Answer

$$0.090$$

Question 4

If $$A$$ and $$B$$ are mutually exclusive events, which of the following is true?

Accepted Answer

$$P(A \cap B) = 0$$

Question 5

A Venn diagram shows two overlapping circles labeled $$A$$ and $$B. $$What does the shaded intersection represent?

Accepted Answer

$$A \cap B$$

Question 6

A grocery store owner estimates that 37 out of 50 customers live within 3 miles of the store. What is the probability that a randomly selected customer does NOT live within 3 miles?

Accepted Answer

$$\frac{13}{50}$$

Question 7

Which formula correctly represents the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 8

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 9

Given $$P(A) = 0.6$$ and $$P(B|A) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.3$$

Question 10

A study shows 55% of executives cheated at golf, and 20% cheated at golf and lied in business. What is the probability that an executive who cheated at golf also lied in business?

Accepted Answer

$$0.364$$

Question 11

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) \cdot P(B)$$

Question 12

A die is rolled. Let $$A be $$the event 'even number' and $$B be$$ 'number less than or equal to 4'. Are $$A$$ and $$B$$ independent?

Accepted Answer

No, because $$P(A \cap B) 
eq P(A) \cdot P(B)$$

Question 13

A professor is assigning pairs from 4 students: Amy, John, Bob, and Sue. How many unique pairs can be formed?

Accepted Answer

$$6$$

Question 14

Suppose you select 5 business ventures from 20. How many different samples of 5 can be selected?

Accepted Answer

$$\binom{20}{5}$$

Question 15

If $$P(A) = 0.3$$, what is the probability of the complement of $$A$$?

Accepted Answer

$$0.7$$

Question 16

In a health insurance survey, what is the probability that a randomly selected person has no health insurance and is aged 18-44? (Use the table: 27,420 out of 332,833)

Accepted Answer

$$0.082$$

Question 17

If $$P(A) = 0.4$$ and $$P(B) = 0.6$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.4 + 0.6 = 1.0$$

Question 18

Which of the following best describes a sample space?

Accepted Answer

A collection of all possible outcomes of an experiment

Question 19

If $$P(A) = 0.5$$, $$P(B) = 0.4$$, and $$P(A \cap B) = 0.2$$, what is $$P(A|B)$$?

Accepted Answer

$$0.5$$

Chapter 3: Probability – Structured Study Notes for Business Statistics

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