Statistics help, probability tree diagram

[tweety1234]

Homework Statement

At the start of a gameshow there are 10 contestants of which 6 are female. In each round of
the game, one contestant is eliminated. All of the contestants have the same chance of
progressing to the next round each time.
(a) Show that the probability that the first two contestants to be eliminated are
both male is 2/15

(b) Find the probability that more females than males are eliminated in the first three
rounds of the game.

(c) Given that the first contestant to be eliminated is male, find the probability that the next
two contestants to be eliminated are both female.

Please can someone help me with this question, I am really stuck. I have drawn a tree diagram but I don't think it is correct, as it does not give the right answer. Can someone have a look at it and show me were I have gone wrong? Or show me what the tree diagram should look like.

from my tree diagram I get the answer for questions 'c'

(\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8} )+ ( \frac{6}{10} \times \frac{4}{9} \times \frac{5}{8}) + (\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8} ) + (\frac{4}{10} \times \frac{6}{9} \times \frac{5}{8} )




thank you!



btw- 'E'- stands for elimnated
NE- stands for not elminated.


http://www.mathhelpforum.com/math-help/attachments/basic-statistics-probability/10795d1238940269-tree-diagram-probability-untitled.jpg

 

[cristo]

You seem to be summing up too many branches. Look back at your tree: instead of saying 'E and NE' it should be 'female eliminated and male eliminated' (to make things clearer). Then, which branch is the one that gives the probability of 'given the first elimination is male, what is the probability the second two are both female'?

 

[tweety1234]

You seem to be summing up too many branches. Look back at your tree: instead of saying 'E and NE' it should be 'female eliminated and male eliminated' (to make things clearer). Then, which branch is the one that gives the probability of 'given the first elimination is male, what is the probability the second two are both female'?

But since its 3 rounds, than should it not be 3 branches? I will re-draw my diagram and post it up.

thank you.