Probability (thanks)?

Question

A bag contains 10 balls, of which 7 are green, 3 white.

A ball is picked of random from bag and its color is noted.

The ball is not replaced.

A second ball is then picked out.

Find the probability that

(a) first ball is green.

(b) first ball is green and second is white.

(c) the balls are of different colors.

Part a I understand how to do.. Answer is 7/10..

Part b... I don't really understand how to do...

Same for part c...

Please help me out, my probability is weak. Thank you (:

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Hmm there's the conditional probabilty that I don't really understand how to use... basically, the rules in probabilty I don't really know how and when to use them..

Answer 1

make yourself a tree diagram and follow the branch which has one green ball picked out.  then from this follow up with a white ball.  so it is 7/10 followed by 3/9.  the end of this branch is 21/90.

for the different colours write out a tree diagram. there are three  branches for the first pick and three branches off each of these three.  Note that the second pick has a denominator of 9 not 10

Answer 2

If you understand part a, then you basically understand this question!

part b) P(1st ball is green) (from part a) is 0.7.

P(2nd ball is white) is 0.33 (3/9) you have 3 white balls and 9 balls left.

so P(2nd is white given first is green) = 0.7 x 0.33 = 0.231

part c) this is probably easiest to understand if you just draw a probability tree, but you can do it without. you have two options - either the first ball is green and the second white, or the first ball is white, and the second green. No other combinations are possible. P(1st green, 2nd white) you already know from part b. P(1st white, 2nd green) is 0.3 x 0.78 = 0.234 (work out same way as part b). Therefore, P(different colours) is 0.231 + 0.234 = 0.465.  

Answer 3

Part a is 7/10

One of the rules for probability is that the probability of getting 'A' and 'B' is the prob. of A * the prob. of B. So P(G) * P(W). So here it will be 7/10 multipilied by 3/10, and whatever you get for that is the answer for b.

For c its the same because if they're different colours it will be the same as part b.