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

Event A = marble is blue

Event B = marble is odd

We are trying to find probability marble is odd, GIVEN it is blue.

There are 4 odd blue marbles (1,3,5,7), so 4/12 marbles are blue and odd

There are 8 blue marbles so 8/12 marbles are blue

Trying to find P(B|A) = P(A and B)/P(A) = (4/12) / (8/12) = 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