Question

The probability of Event A is 40%. The probability of Event B is 60%. The joint probability of AB is 40%. The probability (P) that A or B occurs, or both occur, is closest to:

a) 100%
b) 80%
c) 60%
d) 40%

Answer 1

The probability that either Event A or Event B occurs, or both occur, is found using the formula for the union of events. Given probabilities for A, B, and their joint occurrence, the computation yields 60% as the answer, which corresponds to option (c).

Step-by-step explanation:

The student is asking about the computation of the probability that either Event A occurs, or Event B occurs, or both occur, which is also known as the union of two events in probability theory. To find this, we can use the formula for the union of two events, which is P(A OR B) = P(A) + P(B) - P(A AND B).

Given that the probability of Event A is 40%, the probability of Event B is 60%, and the probability that both events occur together (joint probability) is also 40%, we calculate: P(A OR B) = 0.40 + 0.60 - 0.40 = 0.60 or 60%.

Therefore, the probability that either Event A or Event B occurs, or both occur, is closest to 60%, which makes the correct option (c).

Answer 2

(C) 60%

Step-by-step explanation:

The probability (P) that A or B occurs, or both occur, is calculated using the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Remember that the symbol ∪ means "or" and that the symbol ∩ "and." P(A ∩ B) refers to the joint probability (probability that both events occur).We can plug in the values of A and B into this formula in order to find P(A ∪ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 0.4 + 0.6 - 0.4

P(A ∪ B) = 0.6 = 60%

The correct choice is choice (C), 60%.