D01-36

Question

A jar contains  B  blue balls,  6B + 10  yellow balls, and  2B+5  green balls only. If a ball is randomly selected from the jar, what is the probability of picking a blue or green ball?

A.  \frac{1}{5}  
B.  \frac{1}{4}  
C.  \frac{1}{3}  
D.  \frac{1}{2}  
E.  \frac{2}{3}

Bunuel · Accepted Answer

Official Solution:

A jar contains  B  blue balls,  6B + 10  yellow balls, and  2B+5  green balls only. If a ball is randomly selected from the jar, what is the probability of picking a blue or green ball?

A.  \frac{1}{5}  
B.  \frac{1}{4}  
C.  \frac{1}{3}  
D.  \frac{1}{2}  
E.  \frac{2}{3}

The total number of balls in the jar is  B + (6B + 10) + (2B + 5) = 9B + 15 .
 
The total number of blue or green balls in the jar is  B + (2B + 5) = 3B + 5 .
 
The probability of picking a blue or green ball is given by  \frac{3B + 5}{9B + 15} = \frac{3B + 5}{3(3B + 5)} = \frac{1}{3} .

Answer: C

Mo2men · Answer

Hi,

As Probability is ratio between two things so we can plug-in number to make it easy.

Put B=1

We have 1 blue, 16 Yellow, 7 green, total balls= 24

We need prob. of choosing blue or green

Prob of choosing  blue  = 1/24

Prob of choosing  green  = 7/24

Prob of choosing  Blue   OR  Green = 1/24 +7/24 = 8/24 =1/3

Answer is C

I hope it helps

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

MyNameisFritz · Answer

I solved this question simply by substituting numbers.

Let's say B = 10
6B+10=70
2B+5=25

Total number of balls: 105

The probability of picking or green = (blue+green)/(total number of balls)=(10+25)/105=1/3

Answer C

sristiiiiiiiii · Answer