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 and B)^c=

Answer 1

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, $$P(A\text{ and }B{)}^c=0.85$$