Question

A box contains 5 purple marbles, 3 green marbles, and 2 orange marbles. Twoconsecutive draws are made from the box without replacement of the first draw.Find the following probability:P(first marble is purple, second is any color EXCEPT purple)

Answer 1

SOLUTION:

We want to find the probability that;

$P(1st\text{ }Purple\text{ }and\text{ }2nd\text{ }Not\text{ }Purple)$$\begin{gathered} P(1st\text{ }Purple)=\frac{5}{10}=\frac{1}{2} \\ P(2nd\text{ not purple\rparen}=\frac{5}{9} \end{gathered}$

Thus;

$P(1st\text{ }purple\text{ }&\text{ }2nd\text{ }not\text{ }purple)=\frac{1}{2}\times\frac{5}{9}=\frac{5}{18}$

Thus, the answer is;

$\frac{5}{18}$