If there are 30 red and blue marbles in a jar, and the ratio of red to

Question

If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, the second marble is red, if you do not return the marbles after each draw?

A. 22/145
B. 1/25
C. 2/25
D. 2/5
E. 3/5

A. 22/145
B. 1/25
C. 2/25
D. 2/5
E. 3/5

CrackverbalGMAT · Answer

Number of Red Marbles = (2 / 5) * 30 = 12

Number of Blue Marbles = 30 - 12 = 18

Probability = Favorable / Total Outcomes

Picking without replacement, and we need to find the probability that the second marble is red.

Case 1: First Red and then 2nd Red: = (12 / 30) * (11 / 29) = 22/145

Case 2: First Blue and then 2nd Red: = (18 / 30) * (12 / 29) = 36/145

Since these are 2 separate events (Case 1 or Case 2), the required probability is the addition of the 2 probabilities = 22/145 + 36/145 = 58/145 = 2 / 5 (Both divisible by 29)

Option D

Arun Kumar

ScottTargetTestPrep · Answer

Solution: 
 
We see that there are 12 red and 18 marbles in the jar before any draws (notice that 12 + 18 = 30 and 12:18 = 2:3). Furthermore, the first marble could be either red or blue.

If the first marble is red, then the probability of drawing a red marble followed by a red marble without replacement is 12/30 x 11/29 = 2/5 x 11/29 = 22/145.

If the first marble is blue, then the probability of drawing a blue marble followed by a red marble without replacement is 18/30 x 12/29 = 3/5 x 12/29 = 36/145.

Therefore, the probability the second marble is red without replacement is 22/145 + 36/145 = 58/145 = 2/5.

Answer: D

SaquibHGMATWhiz · Answer

Solution:

Number of red balls  =\frac{2}{2+3}	imes 30=12  
 Number of blue marbles  =\frac{3}{2+3}	imes 30=18  
 Total cases of picking 2 marbles without replacing  =30	imes 29=870  
 Favorable case 1: 1st marble red and 2nd marble also red  = 12	imes 11=132  
 Favorable case 2: 1st marble blue and 2nd marble red  =18	imes 12=216  
 Required probability  =\frac{Favorable case 1 + Favorable case 2}{Total cases} = \frac{132+216}{870}=\frac{348}{870}=\frac{2}{5}

Hence the right answer is    Option D

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If there are 30 red and blue marbles in a jar, and the ratio of red to

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