Conditional probability and multiplication rule

Question

A jar contains four red marbles number 1 to 4 and 10 blue marbles numbered 1 to 10 marvelous, chosen at random if you’re told the marvels blue what is the probability that it has the number three on it

Answer 1

Let's consider our sample space. We have four red marbles numbered 1-4 and ten blue marbles numbered 1-10. Given that we know the chosen marble is blue, we can focus in on the number of blue marbles. We know that there are 10 blue marbles and only one of them contains the number 3 on it. So, we conclude that

P(number 3 on the marble | marble is blue) = 1/10 = 0.1

Another way we can do this is to let A be the event that we see a number 3 on the marble and let B be the event that the marble is blue.

We can also do this as P(A | B) = P(A ∩ B) / P(B) = 1/10 = 0.1

Hope this helped!