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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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Re: If there are 30 red and blue marbles in a jar, and the ratio of red to [#permalink]
Bunuel wrote:
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

Solution:

• Number of red balls $$=\frac{2}{2+3}\times 30=12$$
• Number of blue marbles $$=\frac{3}{2+3}\times 30=18$$
• Total cases of picking 2 marbles without replacing $$=30\times 29=870$$
• Favorable case 1: 1st marble red and 2nd marble also red $$= 12\times 11=132$$
• Favorable case 2: 1st marble blue and 2nd marble red $$=18\times 12=216$$
• 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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Re: If there are 30 red and blue marbles in a jar, and the ratio of red to [#permalink]
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Re: If there are 30 red and blue marbles in a jar, and the ratio of red to [#permalink]
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