How do I find P(T)? Please help, this is due tonight!

Question

A box of cookies contains 4 chocolate and 6 butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)

1. P(BB) = 30/90
2. P(BC) = 24/90
3. P(CB) = 24/90
4. P(CC) = 12/90

Let T be the event that both cookies selected were different flavors. Find P(T). Use the complement rule and the branches of the tree. The answers should be the same with both methods. (Enter your probability as a fraction.)

Answer 1

Ok, before attacking this problem, we have to consider that the probability of getting two different types of cookies is the sum of the probability of the two different combinations. So, using the branches of tree, we'll start off by saying that the probability of getting a chocolate cookie first is 4/10, and then the probability of getting a butter cookie is 6/9. So:

P(CB)=P(C)*P(B)=4/10*6/9=24/90 and likewise, P(BC)= 6/10*4/9= 24/90. And now that we have the probability of both possibilities, we just add them up and we get 48/90.

The complement rule is much simpler. We know that those probabilities add up to 1, so to find the probability that we get different cookies, we subtract the probabilities that you get the same cookies in both tries from 1.

Effectively, this is our equation:

P(Different Cookies)=1-P(Same Cookies) => 1-P(BB)-P(CC) = 1-12/90-30/90=48/90, which is the same answer we got up above.