Question

A jar contains 8 red marbles, numbered 1 to 8, and 12 blue marbles numbered 1 to 12.

a) A marble is chosen at random. If you're told the marble is blue, what is the probability that it has the number 6 on it?
   

b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 9 on it, what is the probability the marble is blue?

Answer 1

Given:

Number of red marbles = 8 (1 to 8)

Number of blue marbles = 12 (1 to 12 )

Probability = number of favourable outcomes/Total number of outcomes

a) A marble is chosen at random. If you're told the marble is blue, the probability that it has the number 6 on it :

P(Number 6 | Blue) = 1/12 = 0.0833

The required probability is 0.0833

b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 9 on it.

There are 2 marbles with number 9 on it, out of which one is blue so

P( number 9 | blue ) = 1/2 = 0.50

The required probability is 0.50