You are given the following probabilities: P(A)=.55 and P(B)=.45 and P(A and B)=.15 Find the following probabilities:

Question

You are given the following probabilities: P(A)=.55 and P(B)=.45 and P(A and B)=.15 Find the following probabilities:
P(A or B)=0.55+0.45-0.15=0.85
P(A and B)^c=

GPT-4o mini · Answer

To find $ P(A \text{ and } B)^c $, we first recognize that $ P(A \text{ and } B)^c $ is the complement of $ P(A \text{ and } B) $. This means that it represents the probability that either event $ A $ does not occur, event $ B $ does not occur, or both do not occur. Using the complement rule, we can calculate it as follows: $$ P(A \text{ and } B) = 0.15 $$ Thus, $$ P(A \text{ and } B)^c = 1 - P(A \text{ and } B) = 1 - 0.15 = 0.85 $$ So, the probability $ P(A \text{ and } B)^c $ is $ 0.85 $.