63.5k views
3 votes
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?

User Wasabigeek
by
8.2k points

1 Answer

2 votes
A)
(x(x+4))/((2x+4)(2x+3))
B) 1/4 = 25%
C) 1/8 = 12.5%

Step-by-step 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

(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

(x)/(2x+4-1)=(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

(x+4)/(2x+4)* (x)/(2x+3)=(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%
User Adriane
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories