The following probabilities are given about events A and B in a sample space: P(A) = 0.30, P(B) = 0.40, P(A or B) = 0.60. We can say that:
A)P(A∩B) = 0.70.
B)P(A) = P(A∩B).
C)P(A∩B) = 0.10.
D)A and B are independent events.

Question

Quizplus · Accepted Answer

The probability of A or B can be calculated as P(A or B) = P(A) + P(B) - P(A∩B). Plugging in the given values, we have 0.6 = 0.3 + 0.4 - P(A∩B), which gives us P(A∩B) = 0.1. Therefore, option C is correct. Option A is incorrect because it suggests that P(A∩B) = 0.7, which would mean that P(A or B) > 1, violating the basic rules of probability. Option B is incorrect because it suggests that P(A) = P(A∩B), which is not generally true unless A and B are mutually exclusive events. Option D cannot be determined from the information given.

The Following Probabilities Are Given About Events a and B