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. x x 4 ________________ 2 x 2 2x 3

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 first pick? 25%

c. What is the probability that Ramon pulls two yellow blocks if there are 6 yellow blocks in the bag before his first pick?

Answer 1

A) $\frac{x(x+4)}{(2x+4)(2x+3)}$
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
$\frac{x+4}{2x+4}$
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 
$\frac{x}{2x+4-1}=\frac{x}{2x+3}$
since there are x yellow blocks, and after 1 is chosen, there are 2x+3 total blocks remaining.

This gives the total probability of 
$\frac{x+4}{2x+4}\times \frac{x}{2x+3}=\frac{x(x+4)}{(2x+4)(2x+3)}$

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%