Suppose that events E and F are independent PE 06 and PF 0

Suppose that events E and F are independent, P(E) = 0.6, and P(F) = 0.7

The probability P(E and F) is _____

About 15% of the population of a large country is hopelessly romantic. If two people are randomly selected.

What is the probability that both will be hopelessly romantic? _____ (Round to four decimal places as needed)

The probability that at least one person is hopelessly romantic is ______ (Round to four decimal places as needed)

Suppose that E and F are two events and that P(E) = 0.3 and P(F/E) = 0.6.

P(E and F) = ______     (Simplify your answer)

The data represent the number of driving fatalities for a certain area by age for male and female drivers.

Age

Male

Female

Under 16

126

128

16-20

5746

2398

21-34

12293

4359

35-54

14891

5457

55-69

5386

2397

70 and over

3479

1161

The probability that a randomly selected driver fatality who was male was 35 to 54 years old is approximately _______    (round to tree decimal places as needed.)

The probability that a randomly selected driver fatality who was 35 to 54 was male is approximately _______    (round to tree decimal places as needed.)

If a victim of a fatal accident aged 35 to 54 more likely to be male or female? Choose the correct answer below.

The driver is more likely to be male because the probability is greater than 0.5.

The driver is more likely to be female because the probability is greater than 0.5.

The driver is more likely to be female because the probability is less than 0.5.

The driver is more likely to be male because the probability is less than 0.5.

Suppose there is a 10.5% probability that a randomly selected person aged 40 years or older is a jogger. In addition, there is a 26.6% probability that a randomly selected person aged 40 years or older is male, given that he or she jogs.

What is the probability that a randomly selected person age 40 or older is a male and jogs _____     (Round to three decimal places as needed)

Would it be unusual? Yes or No

Find the value of the factorial 3! = _____     (Type the whole number)

Fin the value of the permutation. 3P3 = _____   (Type the whole number)

Find the value of the combination 4C4 = _______   (Type the whole number)

Outside a home, there is a 9-key keypad numbered 1 through 9. The correct three-digit code will open the garage door. The numbers can be repeated in the code.

How many codes are possible? ________ (Type an integer or fraction. Simplify your answer)

The probability that the correct code is given on the first try, assuming that the owner doesn’t remember it is _____ (Type an integer or fraction. Simplify your answer)

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of seven students and eight faculty.

What is the probability of selecting a jury of all students?

What is the probability of selecting a jury of all faculty?

What is the probability of selecting a jury of 3 students and 2 faculty?

Age	Male	Female
Under 16	126	128
16-20	5746	2398
21-34	12293	4359
35-54	14891	5457
55-69	5386	2397
70 and over	3479	1161

Solution

Suppose that events E and F are independent, P(E) = 0.6, and P(F) = 0.7
The probability P(E and F) is _____

If E and F are independent, then

P(E and F) = P(E) P(F)

Thus,

P(E and F) = 0.6*0.7 = 0.42 [ANSWER]

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About 15% of the population of a large country is hopelessly romantic. If two people are randomly selected.

What is the probability that both will be hopelessly romantic? _____ (Round to four decimal places as needed)

P(both) = 0.15*0.15 = 0.0225 [answer]

The probability that at least one person is hopelessly romantic is ______ (Round to four decimal places as needed)

P(at least one) = 1 - P(both are not) = 1 - (1-0.15)^2 = 0.2775 [ANSWER]

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