Given the following: P(A) = 0.3 P(B) = 0.2 P(A or B) = 0.5 P(A and B) = 0 Which of the following is true? A and B are disjoint. A and B are neither disjoint nor independent. A and B are independent. A and B are disjoint and independent.

Question
Given the following: P(A) = 0.3 P(B) = 0.2 P(A or B) = 0.5 P(A and B) = 0
Which of the following is true?
A and B are disjoint.
A and B are neither disjoint nor independent.
A and B are independent.
A and B are disjoint and independent.

Answers (1)

2021-01-09
Given: P(A) = 0.3
P(B) = 0.2
P(A or B) = 0.5
P(A and B) = 0
Two events are disjoint, if the events cannot occur at the same time. Since P(A and B) = 0, the events A and B cannot occur at the same time and thus events A and B are disjoint.
Two events are independent, if the probability that one event occur in no way affects the probability of the other event ocuring.
Moreover, two events are intependent if and only if P(A and B) = P(A) * P(B).
P(A) * P(B) = 0.3 * 02 = 0.06
P(A and B) = 0
Since 0.06 ≠ 0, the events A and B are not independent. Thus the answer is then: A and B are disjoint.
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