Carcass wrote:
A certain jar contains 5 marbles, r of which are red. If two marbles are to be selected at random, and the probability that both marbles will be red is \(\frac{1}{10}\) , what is the value of r?
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Approach 1Number of ways of picking \(2\) marbles from \(r\) is \(^rC_2\)
Total number of ways of picking \(2\) marbles from \(5\) is \(^5C_2\)
So, \(\frac{^rC_2}{^5C_2} = \frac{1}{10}\)
Upon solving further;
\(r(r-1) = 2\)
\(r^2 - r - 2 = 0\)
\((r+1)(r-2) = 0\)
i.e. \(r = -1 or 2\)
\(r\) can only be \(2\)
Approach 2Plug in the values
A. \(\frac{^1C_2}{^5C_2}\), doesn't make sense! How can we pick 2 marbles when there is only 1?B. \(\frac{^2C_2}{^5C_2} = \frac{1}{10}\), we have our answer!Don't need to check
C, D, and EHence, option B