# Conditional probability:$n$ black and red marbles

In a bag we have 5 red marbles and 3 white

We assume they are identical We pick from the bag randomly 3 marbles at the same time

1. Calculate the probability of the events:

-A:"picking three reds"

-B:"picking at least one white "

2. We replace the white marbles in the bag with $$n$$ Black marbles ($$n$$ > 1) We pick 2 marbles (one after one) without replacement

a) calculate the probability of picking red at the second picking

b) if the second marble picked is red, what is the the probability that the first one is black

• What have you tried? This is pretty standard conditional probability. – Don Thousand Mar 25 '19 at 23:02
• @DonThousand the first question is easy , 2.b) I have problem in calculating intersections of events – Abdennour Harche Mar 25 '19 at 23:11
• If you post what you have tried, we may see what the trouble might be. But here's a hint: If the second marble is red, then the first marble could not have been that particular red marble. – Graham Kemp Mar 26 '19 at 0:24