Question

9 multiple choice 4 points select the most appropriate response. an event a will occur with probability 0.4. an event b will occur with probability 0.6. the probability that both a and b will occur is 0.20. we may conclude that events a and b are independent. that events a and b are dependent. that either a or b always occurs. that events a and b are mutually exclusive.

Explanation:

Step1: Recall independence formula

For two events $A$ and $B$, if they are independent, $P(A\cap B)=P(A)\times P(B)$.

Step2: Calculate $P(A)\times P(B)$

Given $P(A) = 0.4$ and $P(B)=0.6$, then $P(A)\times P(B)=0.4\times0.6 = 0.24$.

Step3: Compare with $P(A\cap B)$

We know $P(A\cap B)=0.20$. Since $P(A\cap B)
eq P(A)\times P(B)$, the events are dependent.

Step4: Analyze other concepts

Mutually - exclusive events have $P(A\cap B) = 0$, which is not the case here. And $P(A)+P(B)=0.4 + 0.6=1$, but just because the sum of probabilities is 1 doesn't mean either $A$ or $B$ always occurs in a non - trivial way related to the given $P(A\cap B)$.

Answer:

that events $A$ and $B$ are dependent.