Question

In a freshman class of 80 students,22 students take Consumer Education,20 students take French,and 4 students take both.Which equation can be used to find the probability,P, that a randomly selected student from this class takes Consumer Education, French,or both?
A: P = 11/40 + 1/4 + 1/20

B: P = 11/40 + 1/4

C: P = 11/40 + 1/4 - 1/20

D: P = 11/40 + 1/4 - 1/10

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Answer 1

Answer: Choice C

P = 11/40 + 1/4 - 1/20

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Explanation:

The formula we use is

P(A or B) = P(A) + P(B) - P(A and B)

In this case,

• P(A) = 22/80 = 11/40 = probability of picking someone from consumer education
• P(B) = 20/80 = 1/4 = probability of picking someone taking French
• P(A and B) = 4/80 = 1/20 = probability of picking someone taking both classes

So,

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 11/40 + 1/4 - 1/20

which is why choice C is the answer

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Note: P(A and B) = 1/20 which is nonzero, so events A and B are not mutually exclusive.