Question

A jar contains 11 red marbles numbered 1 to 11 and 18 blue marbles numbered 1 to 18. A marble is drawn at randomfrom the jar.a. Find the probability the marble is odd given that it is blue.

Answer 1

The Conditional probability formula states that 'the probability of A given event B is'

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Therefore, in our case, the probability of a marble being odd given that it is blue is

$P(odd|blue)=\frac{P(odd\cap blue)}{P(blue)}=\frac{\frac{9}{11+18}}{\frac{18}{11+18}}$

Simplifying,

$\Rightarrow P(odd|blue)=\frac{9}{18}=\frac{1}{2}$

Thus, the probability the marble is odd given that it is blue is 1/2. The answer is 1/2.