Q: A bag contains 810 scales, 102 of which are defective. If two scales are selected with replacement, what is the probability that both are defective?

$$\frac{102}{810} \times \frac{102}{810} = 0.0159$$

Q: A bag contains 810 scales, 102 of which are defective. If two scales are selected without replacement, what is the probability that both are defective?

$$\frac{102}{810} \times \frac{101}{809} = 0.0157$$

Q: If two subjects are randomly selected without replacement from a group of 1000, where 134 had positive test results, what is the probability that both had positive test results?

$$\frac{134}{1000} \times \frac{133}{999} = 0.0178$$

Question 1

Which of the following best describes the sample space $$S in $$probability theory?

Accepted Answer

The set of all possible outcomes of an experiment.

Question 2

Suppose you roll a fair six-sided die. Let $$A be $$the event 'rolling an even number.' What is the complement of $$A$$?

Accepted Answer

$$\{1, 3, 5\}$$

Question 3

A spinner is divided into 8 equal sections labeled $$1$$ through $$8. $$What is the probability of spinning a number less than $$6$$?

Accepted Answer

$$\frac{5}{8}$$

Question 4

Given events $$A$$ and $$B$$ with $$A \subseteq B$$, which of the following statements is true?

Accepted Answer

Every outcome in $$A is $$also in $$B.$$

Question 5

If $$A$$ and $$B$$ are mutually exclusive events, what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 6

A survey of 1000 adults found 44 who used a drug and tested positive, 6 who used a drug and tested negative, 90 who did not use a drug and tested positive, and 860 who did not use a drug and tested negative. What is the probability that a randomly selected adult either used the drug or tested positive?

Accepted Answer

$$\frac{44 + 90 + 6}{1000} = 0.14$$

Question 7

Which formula correctly expresses the addition rule for any two events $$A$$ and $$B$$?

Accepted Answer

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

Question 8

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

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

Question 9

A bag contains 810 scales, 102 of which are defective. If two scales are selected with replacement, what is the probability that both are defective?

Accepted Answer

$$\frac{102}{810} 	imes \frac{102}{810} = 0.0159$$

Question 10

A bag contains 810 scales, 102 of which are defective. If two scales are selected without replacement, what is the probability that both are defective?

Accepted Answer

$$\frac{102}{810} 	imes \frac{101}{809} = 0.0157$$

Question 11

Suppose in a group of 20 people, 13 are female and 7 are male. If 8 own a pet, and 5 of those are female, what is the probability that a randomly selected person is a female who owns a pet?

Accepted Answer

$$\frac{5}{20} = 0.25$$

Question 12

Given the following contingency table for voter registration: 300 males and 600 females are Democrats, 500 males and 300 females are Republicans, 200 males and 100 females are Other. What is the probability that a randomly selected Democrat is male?

Accepted Answer

$$\frac{300}{900} = 0.333$$

Question 13

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 14

A recent survey found that 202 out of 1010 adults smoke. What is the probability that a randomly selected adult does NOT smoke?

Accepted Answer

$$1 - \frac{202}{1010} = 0.8$$

Question 15

Suppose three children are born. What is the probability that all three are of the same gender, assuming boys and girls are equally likely?

Accepted Answer

$$\frac{2}{8} = 0.25$$

Question 16

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.3 + 0.4 - 0.1 = 0.6$$

Question 17

In a Titanic dataset, there are 197 first-class survivors and 122 first-class deaths. What is the probability that a randomly selected first-class passenger survived?

Accepted Answer

$$\frac{197}{197 + 122} = 0.618$$

Question 18

If two subjects are randomly selected without replacement from a group of 1000, where 134 had positive test results, what is the probability that both had positive test results?

Accepted Answer

$$\frac{134}{1000} 	imes \frac{133}{999} = 0.0178$$

Chapter 4: Probability – Concepts, Rules, and Applications

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