To find \( P(A \text{ and } B)^c \), we can use the concept of the complement of an event. The complement of the event \( A \text{ and } B \) is represented as \( (A \text{ and } B)^c \), which includes all outcomes that are not in the event \( A \text{ and } B \).
We know that the probability of the complement of an event can be calculated as: \[ P(E^c) = 1 - P(E) \]
In this case, \( E \) is \( A \text{ and } B \). Therefore: \[ P(A \text{ and } B)^c = 1 - P(A \text{ and } B) \]
Given that \( P(A \text{ and } B) = 0.15 \), we can substitute to find \( P(A \text{ and } B)^c \): \[ P(A \text{ and } B)^c = 1 - 0.15 = 0.85 \]
Thus, \[ P(A \text{ and } B)^c = 0.85 \]
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