# Probability: independent or not?

• Nov 21st 2011, 01:32 AM
Punch
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.
• Nov 21st 2011, 11:51 AM
takatok
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.
• Nov 22nd 2011, 05:29 AM
Flatiron
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).