Consider randomly selecting a student at X school. Let A denote the event that t

Question

Consider randomly selecting a student at X school. Let A denote the event that the selected student has a math class and let B be the event that the selected student has a chemistry class. Suppose that P(A) = 0.6 and P(B) = 0.5.

(a) Is it possible that P(A B) = 0.55? Cite a theorem of probability in your answer.

(b) For the remaining questions, let P(A B) = 0.3. Compute the probability that the selected individual has at least one of the two types of classes.

(c) What is the probability that the selected individual has neither type of class?

(d) Describe in terms of A and B the event that the selected student has math but not chemistry, and then calculate the probability of this event.

Explanation / Answer

a) No, it is not possible that P(A B) = 0.55 because:

P(A B) < Min{P(A), P(B)}

b) P(At least one)

= P(A U B)

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

= 0.6 + 0.5 - 0.3

= 0.8

c) P(Neither) = 1 - P(At least 1) = 1 - 0.80 = 0.20

d) P(Math but not chemistry)

= P(A B')

= P(A) - P(A B)

= 0.6 - 0.3

= 0.3

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