Q: Which formula is used to compute the probability of an event using the classical method?

$$P(E) = \frac{\text{Number of outcomes in } E}{\text{Total number of outcomes}}$$

Question 1

Which of the following best describes the sample space for rolling a fair six-sided die?

Accepted Answer

$$\{1, 2, 3, 4, 5, 6\}$$

Question 2

Suppose you roll a fair die and then flip a coin. How many possible outcomes are there in the sample space?

Accepted Answer

$$12$$

Question 3

Which of the following is NOT a rule for a probability distribution?

Accepted Answer

The sum of all probabilities must be less than 1.

Question 4

Given the following probability distribution for seatbelt use: $$P(	ext{Always}) = 0.684$$, $$P(	ext{Most times}) = 0.158$$, $$P(	ext{Sometimes}) = 0.076$$, $$P(	ext{Rarely}) = 0.055$$, $$P(	ext{Never}) = 0.026. Is it $$unusual for a college student to never wear a seatbelt while driving?

Accepted Answer

Yes, because the probability is less than $$0.05.$$

Question 5

If you roll a fair six-sided die 100 times and get a four 21 times, what is the empirical probability of rolling a four?

Accepted Answer

$$\frac{21}{100} = 0.21$$

Question 6

A bag contains 40 red tulip bulbs and 35 yellow tulip bulbs. What is the probability of randomly selecting a yellow tulip bulb?

Accepted Answer

$$\frac{35}{75} \approx 0.467$$

Question 7

Which of the following events is considered 'unusual' in probability?

Accepted Answer

An event with probability less than $$0.05$$

Question 8

If the probability of event $$E is$$ $$0.3$$, what is the probability of event $$E$$ not occurring?

Accepted Answer

$$0.7$$

Question 9

A probability experiment consists of flipping a coin and rolling a die. What is the probability of getting heads and a 3?

Accepted Answer

$$\frac{1}{12}$$

Question 10

Which of the following sets represents the event 'rolling an even number' on a six-sided die?

Accepted Answer

$$\{2, 4, 6\}$$

Question 11

If three numbers in the set $$\{1, 2, 3, 4, 5, 6\}$$ are divisible by 3, what is the probability of randomly selecting a number divisible by 3?

Accepted Answer

Question 12

Which of the following is a valid probability distribution?

Accepted Answer

Probabilities: $$0.2$$, $$0.3$$, $$0.5$$

Question 13

If you observe an event $$E 40 $$times out of 200 trials, what is the empirical probability of $$E$$?

Accepted Answer

$$\frac{40}{200} = 0.2$$

Question 14

A probability distribution is constructed from survey data. If the sum of the probabilities is $$0.95$$, what does this indicate?

Accepted Answer

It is not a valid probability distribution.

Question 15

Which formula is used to compute the probability of an event using the classical method?

Accepted Answer

$$P(E) = \frac{	ext{Number of outcomes in } E}{	ext{Total number of outcomes}}$$

Question 16

In a probability experiment, which of the following best describes an 'event'?

Accepted Answer

Any subset of the sample space.

Question 17

If the probability of selecting a red tulip bulb from a bag is $$0.53$$, what is the probability of not selecting a red tulip bulb?

Accepted Answer

$$0.47$$

Question 18

Which of the following is the correct interpretation of a probability of $$0.375$$ for an event?

Accepted Answer

The event is expected to occur $$37.5\% of $$the time in repeated trials.

Question 19

A survey of 4521 students found that 111 never wear a seatbelt. What is the relative frequency probability that a randomly selected student never wears a seatbelt?

Accepted Answer

$$\frac{111}{4521} \approx 0.025$$

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