Mathematics Help?

Question

Hello. I need desperate help on how to show and solve both of these questions.

Mathematics Help?
If possible I would like help with this equation:


Ted has two large identical dice painted so that 4 faces are blue and two faces are red. He rolls the two dice and observes how many blue faces are uppermost.
a)Complete the tree diagram, including probabilities and outcomes possible, to represent this situation.
b)Using you tree diagram, or otherwise, calculate the probability that the two faces are different colours

How Would I solve and find the answer? The tree diagram that i am supposed to represent the situation on is here:

http://www.freeimagehosting.net/image.php?f7aadaf2c3.jpg

Please Help as I need desperate help with this.
Thankyou.

Answer 1

The tree starts with die 1. You can roll a blue-up with a probability of 2/3 and a blue-down with a probability of 1/3. Those are your two outcomes. If you now throw the second die, you have the same outcomes, but the second die outcomes have to be connected with the first die outcome.
So your die-one "blue-up" leg will have two die-two outcomes, a "blue-up" with prob of 2/3, and a "blue-down" with prob of 1/3. Then, the probability of the 2 events (2 blue-ups) and (1 blue-up followed by a blue-down) are 4/9 and 2/9.

Further, your die-one "blue down" leg will have two die-two outcomes. So the probability of a blue-down followed by a blue-up is 1/3 * 2/3 = 2/9, and of a blue-down followed by a second blue-down is 1/9.

That's the info in your tree diagram. To get your probability, you need the probability of blue-up followed by blue-down and blue-down followed by blue-up. Going back thru the above discussion, the probability is 4/9th

Answer 2

answer:

1)http://www.freeimagehosting.net/image.php?1126c03302.jpg

2)probability = (blue:red) or (red:blue)

= 2/9 + 2/9

= 4/9

i hope i can help....

Answer 3

a)
Die 1_____Die 2

(Red) 2/6
_________(Red) 2/6 ... RR: 2/6 * 2/6 = 11.11..%
_________(Blue) 4/6 ... RB: 2/6 * 4/6 = 22.22..%

(Blue) 4/6
_________(Red) 2/6 ... BR: 4/6 * 2/6 = 22.22..%
_________(Blue) 4/6 ... BB: 4/6 * 4/6 = 44.44..%

b)
Probability that two faces are different colours = RB + BR = (2/6 * 4/6) + (4/6 * 2/6) = 16/36 = 4/9 = 44.44..%