Find the probability that

Question

From a box there are 6 white balls and 4 red balls, then 4 balls are selected, without replacement, at random and transferred to a second box, which is empty.

balls are selected at random and transferred to a second urn, which is empty.

After that two balls are randomly selected, without replacement, from the second box.

If among the 4 balls transferred there are at least 2 white balls, calculate the probability that the two balls selected from the second box are both white.

Answer 1

First find the probabilities of picking four with two whites, three whites, and four whites. That's the condition.

Then find the probabilities of picking two whites from each of those three scenarios.

Add those and take it out of the conditional probability.

Done.