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

Question

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

Infinity Learn · Accepted Answer

Let the number of green socks are x > $$0$$ E : two socks drawn are of the same color ⇒$$P(E)=P(RR$$ or BB or WW or $$GG)=3C2$$   $$6+x+C2$$   $$xC2$$   $$6+x$$  $$=6(x+6)(x+5)+x(x$$−$$1)(x+6)(x+5)$$ $$=15($$ given $$)$$⇒$$5x2$$−$$x+6=x2+11x+30$$⇒$$4x2$$−$$16x=0$$⇒ $$x=4$$

Theorems of probability

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

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Theorems of probability

Remember concepts with our Masterclasses.

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

Let the number of green socks are x > 0 E : two socks drawn are of the same color ⇒P(E)=P(RR or BB or WW or GG)=3C2 6+x+C2 xC2 6+x =6(x+6)(x+5)+x(x−1)(x+6)(x+5) =15( given )⇒5x2−x+6=x2+11x+30⇒4x2−16x=0⇒ x=4

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