A)
![\frac{x(x+4)}{(2x+4)(2x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%28x%2B4%29%7D%7B%282x%2B4%29%282x%2B3%29%7D)
B) 1/4 = 25%
C) 1/8 = 12.5%
Explanation
A) Let x = the number of yellow blocks. Then x+4 = the number of red blocks, and x+x+4=2x+4 is the total number of blocks.
The probability of choosing a red block first would be
![\frac{x+4}{2x+4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B4%7D%7B2x%2B4%7D)
since there are x+4 red blocks out of 2x+4 total blocks.
The probability of choosing a yellow block after the red block would be
![\frac{x}{2x+4-1}=\frac{x}{2x+3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2x%2B4-1%7D%3D%5Cfrac%7Bx%7D%7B2x%2B3%7D)
since there are x yellow blocks, and after 1 is chosen, there are 2x+3 total blocks remaining.
This gives the total probability of
![\frac{x+4}{2x+4}\times \frac{x}{2x+3}=\frac{x(x+4)}{(2x+4)(2x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B4%7D%7B2x%2B4%7D%5Ctimes%20%5Cfrac%7Bx%7D%7B2x%2B3%7D%3D%5Cfrac%7Bx%28x%2B4%29%7D%7B%282x%2B4%29%282x%2B3%29%7D)
B) If there are 6 yellow blocks, there are 6+4=10 red blocks, and 10+6=16 total blocks.
The probability of getting a red block first would be 10/16, and the probability of getting a yellow block after the red block would be 6/15. Together this gives us
10/16(6/15) = 60/240 = 1/4 = 0.25 = 25%
C) If there are 6 yellow blocks, there are 6+4=10 red blocks, and 10+6=16 total blocks.
The probability of getting a yellow block first is 6/16, and the probability of getting a second yellow block after the first one is 5/15. Together this gives us
6/16(5/15) = 30/240 = 1/8 = 0.125 = 12.5%