7.) Solve below: 7A. 148 cars were sold during the month of April. 87 had air co

Question

7.) Solve below:

7A.

148 cars were sold during the month of April. 87 had air conditioning and 81 had automatic transmission. 58 had air conditioning only, 52 had automatic transmission only, and 9 had neither of these extras. What is the probability that a randomly selected car had automatic transmission or air conditioning or both?

a) 0.1959

b) 0.7432

c) 0.9392

d) 0.2086

e) 0.5473

f) None of the above.

7B.

A campus radio station surveyed 235 students to determine the types of music they like. The survey revealed that 119 like rock only, 80 like country only and 16 like both of these types of music. What is the probability that a randomly selected student likes country but not rock?

a) 0.0681

b) 0.3653

c) 0.3404

d) 0.4085

e) 0.3743

f) None of the above.

7C.

A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 199 like rock, 155 like country, and 114 like jazz. Moreover, 24 like rock and country, 23 like rock and jazz, 19 like country and jazz, and 8 like all three types of music. What is the probability that a randomly selected student likes exactly one of the three types?

a) 0.2880

b) 0.7200

c) 0.4000

d) 1

e) 0.0160

f) None of the above.

Explanation / Answer

a) P(automatic transmission or air conditioning or both) = 1 - P(neither of these) = 1 - 9/148 = 0.9392

Option-C)

b) P(student likes country but not rock) = P(country only) = 80/235 = 0.3404

Option-C)

c) P(only rock) = P(rock) - P(rock and country) - P(rock and jazz) + P(all three) = 199/500 - 24/500 - 23/500 + 8/500 = 0.32

P(only country) = P(country) - P(rock and country) - P(country and jazz) + P(all three) = 155/500 - 24/500 - 19/500 + 8/500 = 0.24

P(only jazz) = P(jazz) - P(rock and jazz) - P(country and jazz) + P(all three) = 114/500 - 23/500 - 19/500 + 8/500 = 0.16

P(exactly one) = P(only rock) + P(only country) + P(only jazz) = 0.32 + 0.24 + 0.16 = 0.72

Option-B)

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