Probability: independent or not?

A bag contains 4 red counters and 6 green counters. Four counters are drawn at random from the bag, without replacement. State with a reason whether or not the events "at least two green counters are drawn" and "at least one counter of each colour is drawn" are independent.

Re: Probability: independent or not?

It depends on whether your statement above means. If we pull a NEW set of marbles for each event, or we just pull 1 set of marbles and find the probabilities of each. If we pull just one set of 4 marbles then each event, and of course any number of events, are independent of each other.

If we pull 4 marbles and check Event A. Then we pull 4 marbles without replacement and check Event B, they are definitely not independent. The marbles we pulled out during Event A will affect the probabilities we calculate for Event B.

Re: Probability: independent or not?

A: at least two green

B: at least one of each color

To show independence, you need to prove that P(A intersection B) = P(A) x P(B).

These values are easier to calculate if you remember that P(X) = 1 - P(~X).

P(B) = 1 - P(0 green) - P(4 green)

P(A) = 1 - P(0 green) - P(1 green)

P(A intersection B) = 1 - P(0 green) - P(1 green) - P(4 green).