aianjie

 

4、Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of both suffering from allergies and not suffering from allergies?

	Suffer from Allergies	Don't Suffer from Allergies	Total
Smoker	35	25	60
Nonsmoker	55	185	240
Total	90	210	300

A)   0.50.

B)   0.00.

C)   1.00.

D)   0.24.

aianjie

 

The correct answer is B

These are mutually exclusive, so the joint probability is zero.

aianjie

 

5、The probability of a new Wal-Mart being built in town is 64%. If Wal-Mart comes to town, the probability of a new Wendy’s restaurant being built is 90%. What is the probability of a new Wal-Mart and a new Wendy’s restaurant being built?

A) 0.576.

B) 0.675.

C) 0.240.

D) 0.306.

aianjie

 

The correct answer is A

P(AB) = P(A|B) × P(B)

The probability of a new Wal-Mart and a new Wendy’s is equal to the probability of a new Wendy’s “if Wal-Mart” (0.90) times the probability of a new Wal-Mart (0.64). (0.90)(0.64) = 0.576.

aianjie

 

6、A two-sided but very thick coin is expected to land on its edge twice out of every 100 flips. And the probability of face up (heads) and the probability of face down (tails) are equal. When the coin is flipped, the prize is $1 for heads, $2 for tails, and $50 when the coin lands on its edge. What is the expected value of the prize on a single coin toss?

A) $17.67.

B) $2.47.

C) $1.50.

D) $26.50.

aianjie

 

The correct answer is B

Since the probability of the coin landing on its edge is 0.02, the probability of each of the other two events is 0.49. The expected payoff is: (0.02 × $50) + (0.49 × $1) + (0.49 × $2) = $2.47.

aianjie

 

7、The following table summarizes the availability of trucks with air bags and bucket seats at a dealership.

	Bucket Seats	No Bucket Seats	Total
Air Bags	75	50	125
No Air Bags	35	60	95
Total	110	110	220

What is the probability of selecting a truck at random that has either air bags or bucket seats?

A)    34%.

B)    73%.

C)   50%.

D)   107%.

aianjie

 

The correct answer is Bfficeffice" />

The addition rule for probabilities is used to determine the probability of at least one event among two or more events occurring. The probability of each event is added and the joint probability (if the events are not mutually exclusive) is subtracted to arrive at the solution. P(air bags or bucket seats) = P(air bags) + P(bucket seats) ? P(air bags and bucket seats) = (125 / 220) + (110 / 220) ? (75 / 220) = 0.57 + 0.50 ? 0.34 = 0.73 or 73%.

Alternative: 1 ? P(no airbag and no bucket seats) = 1 ? (60 / 220) = 72.7%

aianjie

 

8、If the probability of both a new Wal-Mart and a new Wendy’s being built next month is 68% and the probability of a new Wal-Mart being built is 85%, what is the probability of a new Wendy’s being built if a new Wal-Mart is built?

A) 0.70.

B) 0.80.

C) 0.60.

D) 0.85.

aianjie

 

The correct answer is B

P(AB) = P(A|B) × P(B)

0.68 / 0.85 = 0.80