Question

Suppose P(C) = .048, P(M ∩ C) = .044, and P(M u C) = .524. Find the indicated probability.

P(M')
A) .528
B) .520
C) .480
D) .472

Answer 1

The correct probability of event M not occurring, P(M'), is 0.480, which is found by subtracting the probability of event M from 1 after calculating P(M) using given probabilities of events M and C and their union and intersection.

Step-by-step explanation:

To find the indicated probability P(M'), we need to understand that P(M') represents the probability of event M not occurring. We can use the given probabilities and the principle that the sum of probabilities of an event and its complement is 1. Therefore:

P(M') = 1 - P(M)

However, P(M) is not given directly, but can be found using the formula for the union of two events:

P(M ∪ C) = P(M) + P(C) - P(M ∩ C)

Given that P(C) = 0.048, P(M ∩ C) = 0.044, and P(M ∪ C) = 0.524, we can solve for P(M):

P(M) = P(M ∪ C) + P(M ∩ C) - P(C) = 0.524 + 0.044 - 0.048 = 0.520

Substituting the value of P(M) into the equation for P(M'):

P(M') = 1 - P(M) = 1 - 0.520 = 0.480

Therefore, the correct answer is C) 0.480.