SOLUTION: There are 3 red, 3 white, and 3 green marbles in a bag. Two are drawn at random. Let A be the event that at least one marble is red. Let B be the event that both marbles are the sa

Algebra ->  Probability-and-statistics -> SOLUTION: There are 3 red, 3 white, and 3 green marbles in a bag. Two are drawn at random. Let A be the event that at least one marble is red. Let B be the event that both marbles are the sa      Log On


   

Question 878171: There are 3 red, 3 white, and 3 green marbles in a bag. Two are drawn at random. Let A be the event that at least one marble is red. Let B be the event that both marbles are the same color. What is the probability of
a) P(A&B)
b) P(AUB)
c) Are A and B mutually excusive? Are they independent?
I have the answers to these questions, I just don't understand how you would know how to solve them.. please help, I have a test tomorrow! Thank you so much.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
9M: 3R,3W, 3G
p(at least one red)= P(no red) = 6/9 = 2%2F3
p(same color) =
a)P(A|B) = P(A and B)/P(B)= (6/72)/(1/4) = 24/72 = 4/12 = 1/3
P(A and B) = P(B)P(A|B) = (1/4)(1/3)= 1/12
b)P(A or B) = P(A) + P(B) - P(A and B) = 2%2F3+%2B+1%2F4+-+6%2F72+=+8%2F12+%2B+3%2F12+-+1%2F12+=+10%2F12+=+5%2F6