Question

Given the following probabilities, algebraically determine if Events A and B are:• mutually exclusive or non-mutually exclusive• independent or dependent.P(A) =P(B) 0.75P(A U B)'U0.15

Answer 1

We know that:

`\begin{gathered} P(A\cup B)^(\prime)=1-P(A\cup B) \\ P(A\cup B)^(\prime)=1-P(A)+P(B)-P(A\cap B) \end{gathered}`

Plugging the values given we have that:

`\begin{gathered} 0.15=1-0.8+0.75-P(A\cap B) \\ P(A\cap B)=1-0.8+0.75-0.15 \\ P(A\cap B)=0.8 \end{gathered}`

Now, since the probability of the intersection is not zero this means that the events are non-mutually exclusive.