Q.

There are two red, two blue, two white, and certain number (greater than 0) of green socks in a drawer. If two socks are taken at random from the drawer without replacement, the probability that they are of the same color is 1/5, then the number of green socks are _________.

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answer is 4.

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Detailed Solution

Let the number of green socks be x > 0.E: Two socks drawn are of the same color⇒ P(E)=P(RR or BB or WW or GG)                 =36+xC2+ xC2 6+xC2                =6(x+6)(x+5)+x(x−1)(x+6)(x+5)=15 (given) ⇒ 5x2−x+6=x2+11x+30or 4x2−16x=0or x = 4
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There are two red, two blue, two white, and certain number (greater than 0) of green socks in a drawer. If two socks are taken at random from the drawer without replacement, the probability that they are of the same color is 1/5, then the number of green socks are _________.