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 $$_________$$.

Question

Infinity Learn · Accepted Answer

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 $$=$$ $$4$$

Introduction to probability

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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 _________.

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Introduction to probability

Remember concepts with our Masterclasses.

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 _________.

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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