# For events A, B from a sample space X, :

$\def\Prob{\mathop{\rm Prob}}$

For events $A, B$ from a sample space $X$, label $A^\complement$ the event complementary to $A$ (i.e., $A \cup A^\complement = X, A \cap A^\complement = \emptyset$ ), and $\Prob[A \mid B]$ denotes the probability of $A$, given that B has occurred.

1) Go with two events $A, B$ from a sample space $X$, for which $\Prob[A] = 1/6$ , and $\Prob[A ∪ B] = 2/3$ . If $A$ and $B$ are independent events, calculate the following probabilities:

a) $\Prob[B] =$

b) $\Prob[A \cap B] =$

c) $\Prob[A^\complement] =$

d) $\Prob[B \mid A] =$

I am stuck on how to even do this- any hint to get started will be greatly appreciated. trying to understand it not only looking for answers.

thanks.

Independence means: $\Prob(A\cap B)=\Prob (A)\cdot\Prob(B)$
Also recall: $\Prob(A\cup B)=\Prob(A)+\Prob(B)-\Prob(A\cap B)$