Q.In a jar there are 5 black marbles and 3 green marbles. Two marbles are picked randomly one after the other without replacement. What is the possibility that both the marbles are black? A) $\frac{5}{14}$ B) $\frac{5}{8}$ C) $\frac{5}{8}$ D) $\frac{5}{16}$

Rearranging the conditional probability formula for $P(A\cap B)$ gives the multiplication theorem: $P(A\cap B)=P(A)\cdot P(B/A)=P(B)\cdot P(A/B)$. This is the natural tool whenever two events happen in sequence and the second depends on the outcome of the first - most commonly, drawing items one after another without replacement, where the composition of the remaining pool changes after the first draw. The probability of 'both events happening' is the probability of the first, times the conditional probability of the second given the first has already occurred.