Q: A bag contains 7 red and 6 blue marbles. What is the probability of drawing a red marble first and then a blue marble, without replacement?

$$\frac{7}{13} \times \frac{6}{12}$$

Q: Which of the following best describes the multiplication rule for dependent events?

$$P(A \cap B) = P(A) \times P(B|A)$$

Q: A standard deck of 52 cards: What is the probability that a card player draws two aces in a row if they keep the first card after drawing it (with replacement)?

$$\frac{4}{52} \times \frac{4}{52}$$

Q: A library randomly selects two books from a list of 100. If 62 are fiction and 38 are nonfiction, what is the probability that both selected books are nonfiction?

$$\frac{38}{100} \times \frac{37}{99}$$

Q: A bag contains 5 green and 3 yellow candies. If you draw two candies without replacement, what is the probability that both are green?

$$\frac{5}{8} \times \frac{4}{7}$$

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

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

Q: A box contains 4 red, 5 blue, and 1 green ball. If two balls are drawn one after another without replacement, what is the probability that both are blue?

$$\frac{5}{10} \times \frac{4}{9}$$

Q: If $$P(A) = 0.7$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.35$$, are A and B independent?

Yes, because $$0.7 \times 0.5 = 0.35$$

Question 1

A bag contains 7 red and 6 blue marbles. What is the probability of drawing a red marble first and then a blue marble, without replacement?

Accepted Answer

$$\frac{7}{13} 	imes \frac{6}{12}$$

Question 2

Which of the following best describes the multiplication rule for dependent events?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B|A)$$

Question 3

A standard deck of 52 cards: What is the probability that a card player draws two aces in a row if they keep the first card after drawing it (with replacement)?

Accepted Answer

$$\frac{4}{52} 	imes \frac{4}{52}$$

Question 4

A library randomly selects two books from a list of 100. If 62 are fiction and 38 are nonfiction, what is the probability that both selected books are nonfiction?

Accepted Answer

$$\frac{38}{100} 	imes \frac{37}{99}$$

Question 5

Given $$P(A \cap B) = 0.12$$ and $$P(A) = 0.3$$, what is $$P(B|A)$$?

Accepted Answer

$$\frac{0.12}{0.3} = 0.4$$

Question 6

In a survey of 43 students, 20 have a math major, 15 have a science major, and 8 have both. What is the probability that a randomly selected student has a science major given that they have a math major?

Accepted Answer

$$\frac{8}{20}$$

Question 7

A company is hiring for two positions. Out of 10 applicants, 6 applied for software developer and 4 for data analyst. Of the software developer applicants, 4 have a degree in computer science. What is the probability that a randomly selected candidate with a degree in computer science applied for the software developer position?

Accepted Answer

$$\frac{4}{5}$$

Question 8

If $$P(A) = 0.5$$, $$P(B|A) = 0.3$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.5 	imes 0.3 = 0.15$$

Question 9

About 15% of people in a town own both a cat and a dog. 40% have a dog. What is the probability that someone who owns a dog also owns a cat?

Accepted Answer

$$\frac{0.15}{0.4} = 0.375$$

Question 10

Which of the following is the correct formula for conditional probability?

Accepted Answer

$$P(B|A) = \frac{P(A \cap B)}{P(A)}$$

Question 11

A bag contains 5 green and 3 yellow candies. If you draw two candies without replacement, what is the probability that both are green?

Accepted Answer

$$\frac{5}{8} 	imes \frac{4}{7}$$

Question 12

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

Accepted Answer

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

Question 13

A hospital has 60% of its patients as adults and 25% of all patients are adults with diabetes. What is the probability that a randomly selected adult patient has diabetes?

Accepted Answer

$$\frac{0.25}{0.6} \approx 0.417$$

Question 14

A box contains 4 red, 5 blue, and 1 green ball. If two balls are drawn one after another without replacement, what is the probability that both are blue?

Accepted Answer

$$\frac{5}{10} 	imes \frac{4}{9}$$

Question 15

If $$P(A) = 0.7$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.35$$, are A and B independent?

Accepted Answer

Yes, because $$0.7 	imes 0.5 = 0.35$$

Question 16

A school has 100 students: 60 play soccer, 30 play basketball, and 20 play both. What is the probability that a randomly selected basketball player also plays soccer?

Accepted Answer

$$\frac{20}{30} = \frac{2}{3}$$

Multiplication Rule for Dependent Events and Conditional Probability

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