Question

I have two bags. Bag 1 contains 10 blue marbles, while Bag 2 contains 15 blue marbles. I pick one of the bags at random and add 6 red marbles in it. Then I shake the bag and choose 5 marbles (without replacement) at random from the bag. If there are exactly 2 red marbles among the 5 chosen marbles, what is the probability that I have chosen Bag 1?

Answer 1

Solution:-

Given

Obtain the probability that Bag 1 is chosen, and it contains 2 red marbles among the 5 chosen marbles.

Here,

P(Bag 1) = P(Bag 2)

=  

Obtain the probability of obtaining 2 red marbles out of 5 selected marbles form Bag 1

P(2 red marbles out of 5 marbles | Bag 1) =

=

= 0.412

Obtain the probability of obtaing 2 red marbles out of 5 selected marbles from Bag 2

P(2 red marbles out of 5 marbles | Bag 2) =

=

= 0.335

The required probability is,

Applying Bayes' theorem,

= 0.552

Therefore, the probability that Bag 1 is chosen, and it contains 2 red marbles among the 5 chosen marbles is 0.552