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

Question

P(A or B)=0.55+0.45-0.15=0.85
P(A and B)c=

Answer 1

To find \( P(A \text{ and } B)^c \), we first need to understand what this notation means. \( P(A \text{ and } B)^c \) represents the probability that either event \( A \) does not occur, event \( B \) does not occur, or both do not occur. In other words, it is the probability of the complement of the event \( (A \text{ and } B) \).

We can use the following formula to find the probability of the complement of \( P(A \text{ and } B) \):

\[ P(A \text{ and } B)^c = 1 - P(A \text{ and } B) \]

From the information given, we know:

\[ P(A \text{ and } B) = 0.15 \]

Thus, we can calculate \( P(A \text{ and } B)^c \) as follows:

\[ P(A \text{ and } B)^c = 1 - 0.15 = 0.85 \]

So, the probability \( P(A \text{ and } B)^c \) is \( 0.85 \).