Final answer:
To find P(not B), we use the complementary probability, P(not B) = 1 - P(B). With the given information, P(B) is found to be 0.45. Therefore, P(not B) equals 0.55, making option A the correct answer.
Step-by-step explanation:
The question wants us to find the probability P(not B), which is the complement of the probability of event B occurring. We can use the given probabilities to calculate this.
The formula to find the probability of either event A or B occurring is:
P(A OR B) = P(A) + P(B) − P(A AND B)
We have the values for P(A), P(A OR B), and P(A AND B):
• P(A) = 0.55
• P(A OR B) = 0.7525
• P(A AND B) = 0.2475
By substituting the known values into the formula, we can solve for P(B):
0.7525 = 0.55 + P(B) − 0.2475
P(B) = 0.7525 + 0.2475 − 0.55
P(B) = 1.0000 − 0.55
P(B) = 0.45
Since P(not B) is the complement of P(B), it is calculated as:
P(not B) = 1 − P(B)
P(not B) = 1 − 0.45
P(not B) = 0.55
Hence, the correct answer is A) 0.55.