Two marbles are drawn in succession from a box containing 10 red,...

Given marbles are:

$10 \to R, 30 \to W, 20 \to B, 15 \to O$

We know that, $P\left(E\right) = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Also, $P\left(A\text{and}B\right) = P\left(A\right) \times P\left(B\right)$, where $A\text{and}B$ are independent events.

Probability of drawing first marble red and then white is given by,

$P\left(E\right) = \dfrac{10}{75} \times \dfrac{30}{75}$

$⇒ P\left(E\right) = \dfrac{4}{75}$