Question 1

A probability experiment consists of tossing a coin and rolling a six-sided die. What is the sample space for this experiment, and how many outcomes does it contain?

Accepted Answer

The sample space is $$\{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6\}$$ and contains 12 outcomes.

Question 2

Which of the following is a simple event?

Accepted Answer

Tossing a coin and getting heads.

Question 3

A restaurant offers a dinner special with 5 choices for an appetizer, 10 choices for an entrée, and 4 choices for dessert. How many different dinner combinations are possible?

Accepted Answer

$$5 	imes 10 	imes 4 = 200$$

Question 4

Which of the following best describes empirical probability?

Accepted Answer

Probability based on observations or experiments, calculated as $$P(E) = \frac{f}{n}.$$

Question 5

If the probability of an event $$E is$$ $$0.3$$, what is the probability of the complement of $$E$$?

Accepted Answer

$$0.7$$

Question 6

A company surveys 1504 people and finds that 406 have a positive impression. What is the empirical probability that a randomly selected person has a positive impression?

Accepted Answer

$$\frac{406}{1504} \approx 0.270$$

Question 7

Which of the following is an example of subjective probability?

Accepted Answer

A doctor estimates a 90% chance of recovery for a patient.

Question 8

What is the probability of drawing a king from a standard deck of 52 playing cards?

Accepted Answer

$$\frac{4}{52} = \frac{1}{13}$$

Question 9

A college ID number consists of 8 digits, each from 0 to 9, and digits can be repeated. How many possible ID numbers are there?

Accepted Answer

$$10^8 = 100$$,000,000$$

Question 10

If you roll two six-sided dice, what is the probability that both dice show a 1?

Accepted Answer

$$\frac{1}{36}$$

Question 11

Which of the following statements about probability is TRUE?

Accepted Answer

The probability of an event is always between 0 and 1, inclusive.

Question 12

A spinner has 8 equal sections numbered 1 to 8. What is the probability of spinning an odd number?

Accepted Answer

$$\frac{4}{8} = 0.5$$

Question 13

Which of the following best illustrates the Law of Large Numbers?

Accepted Answer

As you toss a coin more times, the proportion of heads approaches 0.5.

Question 14

If $$P(E) = 0.4$$, what is $$P(E')$$?

Accepted Answer

$$0.6$$

Question 15

A survey of 1000 employees found that 366 are aged 25 to 34. What is the probability that a randomly selected employee is NOT aged 25 to 34?

Accepted Answer

$$1 - \frac{366}{1000} = \frac{634}{1000} = 0.634$$

Question 16

Which of the following is NOT a valid probability value?

Accepted Answer

$$-0.2$$

Question 17

You draw one card from a standard deck of 52 cards. What is the probability of drawing a heart?

Accepted Answer

$$\frac{1}{4}$$

Question 18

A computer randomly selects a number from 1 to 2000. Event A is selecting the number 253. Is this a simple event?

Accepted Answer

Yes, because it consists of a single outcome.

Introductory Statistics: Probability Concepts and Practice Problems

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