Q: A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is either a queen or a black card?

$$P(\text{Queen or Black}) = \frac{15}{26}$$

Q: In a binomial experiment with $$n = 8$$ and $$p = 0.4734$$, what is the expected value (mean) of the number of wins?

$$\mu = 8 \times 0.4734 = 3.787$$

Q: If two cards are drawn in succession without replacement from a standard deck, what is the probability that both cards are black?

$$\frac{26}{52} \times \frac{25}{51}$$

Q: A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is the mean $$\mu of$$ $$X$$?

$$\mu = 1 \times 0.2 + 2 \times 0.5 + 3 \times 0.3 = 2.1$$

Question 1

Which of the following is the correct formula for the probability of the union of two events A and B that are not mutually exclusive?

Accepted Answer

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

Question 2

A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is either a queen or a black card?

Accepted Answer

$$P(	ext{Queen or Black}) = \frac{15}{26}$$

Question 3

Which of the following is NOT a condition for a discrete probability distribution?

Accepted Answer

Each probability must be greater than 1.

Question 4

In a binomial experiment with $$n$$ trials and probability of success $$p$$, what does the random variable $$X$$ represent?

Accepted Answer

The number of successes in $$n$$ trials

Question 5

If the odds of an event $$E$$ are $$7:2$$, what is the probability $$P(E)$$?

Accepted Answer

$$P(E) = \frac{7}{9}$$

Question 6

Which of the following statements is TRUE about the mean of a probability distribution?

Accepted Answer

It represents the long-run average value of the random variable.

Question 7

A six-sided die is rolled 80 times. If the probability of rolling a 1 is $$0.15$$, a 2 is $$0.25$$, a 3 is $$0.10$$, a 4 is $$0.10$$, a 5 is $$0.225$$, and a 6 is $$0.175$$, is this a probability distribution?

Accepted Answer

No, because the probabilities do not sum to 1.

Question 8

In a binomial experiment with $$n = 8$$ and $$p = 0.4734$$, what is the expected value (mean) of the number of wins?

Accepted Answer

$$\mu = 8 	imes 0.4734 = 3.787$$

Question 9

A shipment of 5000 batteries has a 5% defect rate. What is the expected number of defective batteries in the shipment?

Accepted Answer

$$5000 	imes 0.05 = 250$$

Question 10

If two cards are drawn in succession without replacement from a standard deck, what is the probability that both cards are black?

Accepted Answer

$$\frac{26}{52} 	imes \frac{25}{51}$$

Question 11

Which of the following is the correct formula for the variance of a binomial distribution?

Accepted Answer

$$\$$sigma^2$$ = npq$$

Question 12

A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is the mean $$\mu of$$ $$X$$?

Accepted Answer

$$\mu = 1 	imes 0.2 + 2 	imes 0.5 + 3 	imes 0.3 = 2.1$$

Question 13

Which of the following is TRUE about mutually exclusive events?

Accepted Answer

Their intersection is the empty set.

Question 14

A ball is drawn at random from an urn containing 8 red, 4 blue, and 3 green balls. What is the probability that the ball is either red or green?

Accepted Answer

$$\frac{11}{15}$$

Question 15

Which of the following best describes the complement rule in probability?

Accepted Answer

$$P(E^c) = 1 - P(E)$$

Question 16

In a binomial experiment, what does it mean for trials to be independent?

Accepted Answer

The outcome of one trial does not affect the outcome of another.

Question 17

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

Accepted Answer

$$P(A \cap B) = 0.2$$

Question 18

Which of the following is a property of a probability distribution for a discrete random variable?

Accepted Answer

The sum of all probabilities is 1.

Question 19

A standard deck of cards is used. What is the probability of drawing a jack that is red or a queen?

Accepted Answer

$$\frac{5}{26}$$

Introductory Statistics: Probability, Distributions, and Binomial Experiments – Guided Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard