marbles question

Question

A jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is odd-numbered given that the marble is blue.

Answer 1

The key wording is "given that the marble is blue" meaning that you only need to consider the blue marbles.

Here is a table of the situation:

So given that the marble is blue (8 total) the number that are odd is 4 so the probability is 4/8 = 1/2

Answer 2

How many blue marbles are there? 1 - 8 --> 8 marbles

How many odd numbered blue marbles are there? 1,3,5,7 --> 4 odd numbered blue [the numerator]

How many total marbles? 4+ 8 = 12 [the denominator]

So the probability of choosing a odd numbered blue marble = 4/12 --> 33% chance