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)=(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)=(P(odd\cap blue))/(P(blue))=((9)/(11+18))/((18)/(11+18))`

Simplifying,

`\Rightarrow P(odd|blue)=(9)/(18)=(1)/(2)`

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