Q: Which of the following correctly defines the probability of an event $$A$$?

$$P(A) = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}}$$

Q: Suppose $$P(E) = 0.3$$, $$P(F) = 0.5$$, and $$P(E \text{ or } F) = 0.7. $$Are events $$E$$ and $$F$$ mutually exclusive?

No, because $$P(E) + P(F) \u003e P(E \text{ or } F)$$

Q: Suppose $$P(E) = 0.3$$, $$P(F) = 0.5$$, and $$P(E \text{ and } F) = 0. $$Are events $$E$$ and $$F$$ mutually exclusive?

Yes, because $$P(E \text{ and } F) = 0$$

Question 1

Which of the following numbers could represent the probability of an event?

Accepted Answer

$$0.23$$

Question 2

Which of the following correctly defines the probability of an event $$A$$?

Accepted Answer

$$P(A) = \frac{	ext{Number of successful outcomes}}{	ext{Total number of outcomes}}$$

Question 3

A fair coin is tossed twice. What is the probability of getting the same outcome on both tosses?

Accepted Answer

$$\frac{1}{2}$$

Question 4

The statement: "It is known that the probability of hitting a pothole while driving on a certain road is 1%." is an example of which type of probability?

Accepted Answer

Empirical probability

Question 5

Suppose $$P(E) = 0.3$$, $$P(F) = 0.5$$, and $$P(E 	ext{ or } F) = 0.7. $$Are events $$E$$ and $$F$$ mutually exclusive?

Accepted Answer

No, because $$P(E) + P(F) \u003e P(E 	ext{ or } F)$$

Question 6

Suppose $$P(E) = 0.3$$, $$P(F) = 0.5$$, and $$P(E 	ext{ and } F) = 0. $$Are events $$E$$ and $$F$$ mutually exclusive?

Accepted Answer

Yes, because $$P(E 	ext{ and } F) = 0$$

Question 7

A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green balls. If two balls are drawn one after another without replacement, what is the probability that both are red? (Round to the nearest thousandth.)

Accepted Answer

$$0.076$$

Question 8

A game has three outcomes: win ($$0.4$$), tie ($$0.5$$), and loss ($$0.1). $$What is the probability of not winning in a single play?

Accepted Answer

$$0.6$$

Question 9

You are playing roulette at a U.S. casino. The wheel has 18 red, 18 black, and 2 green slots. What is the probability of getting at least one red in 4 spins? (Round to the nearest ten-thousandth.)

Accepted Answer

$$0.8685$$

Question 10

A car is randomly selected from a lot. Given that the car is over 10 years old, what is the probability that it is domestic? (Use the following data: Over 10 years old: 21 foreign, 26 domestic.)

Accepted Answer

$$\frac{26}{47}$$

Question 11

Classify the random variable: The number of goals scored in a hockey game.

Accepted Answer

Discrete

Question 12

Classify the random variable: The speed of a car on a New York tollway during rush hour.

Accepted Answer

Continuous

Question 13

Given the probability distribution: $$x = 0, 1, 2, 3, 4$$ with $$P(x) = 0.02, 0.07, 0.22, 0.27, 0.42$$, does this form a valid probability distribution?

Accepted Answer

Yes, because $$\sum P(x) = 1$$ and $$0 \leq P(x) \leq 1$$ for all $$x$$

Question 14

A seed company plants 50 rows of 40 seeds each. The probability that a row has 36 seeds germinate is $$0.20. $$What is the expected number of rows (out of 50) with exactly 36 seeds germinated?

Accepted Answer

$$10$$

Question 15

Is the following a binomial experiment? Selecting five cards, one at a time without replacement, from a standard deck, counting the number of picture cards.

Accepted Answer

No, because the probability of success changes with each draw

Question 16

The probability that a house in an urban area will develop a leak is $$0.04. If 39 $$houses are randomly selected, what is the probability that none will develop a leak? (Round to the nearest thousandth.)

Accepted Answer

$$0.208$$

Question 17

A quiz has 10 multiple choice questions, each with 5 possible answers. To pass, a student must get at least 6 correct. If a student guesses randomly, what is the probability of passing? (Round to the nearest thousandth.)

Accepted Answer

$$0.013$$

Question 18

According to the FCC, 70% of U.S. households have VCRs. In a random sample of 15 households, what is the probability that between 10 and 12 (inclusive) have VCRs? (Round to the nearest thousandth.)

Accepted Answer

$$0.404$$

Question 19

According to government data, the probability that an adult was never in a museum is $$0.20. In a $$random survey of 70 adults, what is the mean number of adults who were never in a museum?

Accepted Answer

$$14$$

Question 20

According to government data, the probability that an adult was never in a museum is $$0.20. In a $$random survey of 70 adults, what is the standard deviation of the number of adults who were never in a museum? (Round to the nearest thousandth.)

Accepted Answer

$$3.354$$

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