Q: If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, are events A and B independent?

Yes, because $$P(A \cap B) = P(A) \times P(B)$$

Q: If the probability of testing positive on a rapid test is $$0.05$$ and the probability of testing positive on a two-day test is $$0.045$$, what is the probability of testing positive on both tests if the tests are independent?

$$0.05 \times 0.045 = 0.00225$$

Question 1

Which of the following best describes the Law of Large Numbers in probability theory?

Accepted Answer

As the number of trials increases, the empirical probability of an event approaches the theoretical probability.

Question 2

A standard deck of 52 cards contains 26 red cards. What is the probability of drawing a red card at random?

Accepted Answer

$$\frac{26}{52} = 0.5$$

Question 3

If you flip a fair coin twice, what is the probability of getting exactly one heads?

Accepted Answer

$$\frac{2}{4} = 0.5$$

Question 4

Which of the following is an example of empirical probability?

Accepted Answer

Calculating the probability of rolling a 6 on a die after rolling it 100 times and counting the number of sixes.

Question 5

Given a six-sided die, what is the probability of rolling an even number OR a number greater than 2?

Accepted Answer

$$\frac{5}{6}$$

Question 6

If the probability of a person having green eyes is $$0.09$$ and the probability of being male is $$0.49$$, and the probability of being both is $$0.03$$, what is the probability of a person being either male or having green eyes?

Accepted Answer

$$0.09 + 0.49 - 0.03 = 0.55$$

Question 7

A fair six-sided die is rolled. What is the probability of NOT rolling a 4?

Accepted Answer

$$1 - \frac{1}{6} = \frac{5}{6} = 0.83$$

Question 8

Which formula correctly expresses the probability of event A given event B has occurred?

Accepted Answer

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

Question 9

Suppose the probability of a person choosing vanilla cake is $$0.40$$ and the probability of choosing cream cheese icing given vanilla cake is $$0.30. $$What is the probability a person chooses vanilla cake AND cream cheese icing?

Accepted Answer

$$0.40 	imes 0.30 = 0.12$$

Question 10

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, are events A and B independent?

Accepted Answer

Yes, because $$P(A \cap B) = P(A) 	imes P(B)$$

Question 11

A tree diagram is useful for which of the following tasks in probability?

Accepted Answer

Visualizing all possible outcomes and calculating compound probabilities.

Question 12

If you roll a fair six-sided die, what is the probability of rolling an even number given that the number is greater than 2?

Accepted Answer

$$\frac{2}{4} = 0.5$$

Question 13

Which of the following statements about complements is TRUE?

Accepted Answer

The probability of the complement of event A is $$1 - P(A).$$

Question 14

In a study of 831 people, 72 have green eyes. What is the empirical probability that a randomly selected person has green eyes?

Accepted Answer

$$\frac{72}{831} \approx 0.09$$

Question 15

If the probability of drawing a red card from a deck is $$0.5$$, what is the probability of NOT drawing a red card?

Accepted Answer

$$1 - 0.5 = 0.5$$

Question 16

Which of the following is a correct application of the addition rule for probabilities?

Accepted Answer

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

Question 17

If the probability of testing positive on a rapid test is $$0.05$$ and the probability of testing positive on a two-day test is $$0.045$$, what is the probability of testing positive on both tests if the tests are independent?

Accepted Answer

$$0.05 	imes 0.045 = 0.00225$$

Question 18

Which of the following is NOT a property of probability?

Accepted Answer

The sum of all probabilities in a sample space must be greater than 1.

Question 19

If $$P(A|B) = P(A)$$, what does this imply about events A and B?

Accepted Answer

A and B are independent.

Chapter 5: Probability – STAT 201 Elementary Statistics Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard