Ramon is playing a game in which he must pull two blocks out of a bag containing red and yellow blocks. He cannot look, and he cannot replace the block. The bag has 4 more red blocks than yellow blocks.
a) Write and simplify an expression that represents Ramon's probability of picking a red block, then a yellow block.
b) What is the probability that Ramon pulls a red block then a yellow block if there are 6 yellow blocks in the bag before his pick?
c) What is the probability that Ramon pulls two yellow blocks if there are 6 yellow blocks in the bag before his first pick?

Question

Ramon is playing a game in which he must pull two blocks out of a bag containing red and yellow blocks. He cannot look, and he cannot replace the block. The bag has 4 more red blocks than yellow blocks. 
a) Write and simplify an expression that represents Ramon's probability of picking a red block, then a yellow block.
b) What is the probability that Ramon pulls a red block then a yellow block if there are 6 yellow blocks in the bag before his pick?
c) What is the probability that Ramon pulls two yellow blocks if there are 6 yellow blocks in the bag before his first pick?

anonymous · Answer

if the number of yellow blocks is n, then the number of red blocks is n+4 and the total number of blocks is n+n+4=2n+4

probability you pick a red block is
$$\frac{n+4}{2n+4}$$ and then the probability you pick a yellow block given the first is red is 
$$\frac{n}{2n+3}$$ multiply these together and get 
$$\frac{(n+4)n}{(2n+4)(2n+3)}$$

anonymous · Answer

if there are six yellow blocks in the bag then there are ten red ones and the total is 16

anonymous · Answer

probability if red then yellow is 
$$\frac{10}{16}\times \frac{6}{15}$$