# On Daily challenge problem

I answered this Daily challenge problem correct but was marked as incorrect. I will give a proof for my answer below

Assumptions:

• Capacity of candies of the cup is constant.

• Candies are mixed well, i.e. the concentration of candies is uniform all over the jar.

• Candies which are more concentrated are more probable to be selected if you pick any candy randomly from a mixture.

Let the capacity of the cup be of $x$ candies

After first step:

Total candies in Jar $B$=$600+x$

Number of Red candies = $x$

Number of Green candies = $600$

Concentration of Red candies = $C_{AR}=\frac{x}{600+x}$

Concentration of Green candies = $C_{AG}=\frac{600}{600+x}$

Taking one cup of candies from jar $B$:

Number of Green candies in the cup = $J_G=C_{AG} \times x=\frac{600x}{600+x}$

Number of Red candies in the cup = $J_R=C_{AR} \times x=\frac{x^2}{600+x}$

After second step:

Total number of candies in jar $A$=$800$

Number of Red candies=$N_R=800-x+J_R=800-x+\frac{x^2}{600+x}=\frac{800(600+x)-x(600+x)+x^2}{600+x}=\frac{4800+800x-600x\cancel{-x^2+x^2}}{600+x}=\frac{4800+200x}{600+x}$

Number of Green candies = $N_G=J_G=\frac{600x}{600+x}$

Concentration of Red candies = $C_{BR}=\frac{N_R}{800}=\frac{4800+200x}{800(600+x)}$

Concentration of Green candies=$C_{BG}=\frac{N_G}{800}=\frac{600x}{800(600+x)}$

After third step:

Concentration of Red candies in the mixture = $\frac{C_{AR}+C_{BR}}{2}=\frac{1}{2}(\frac{x}{600+x}+\frac{4800+200x}{800(600+x)})=\frac{1}{2}(\frac{800x+4800+200x}{600(800+x)})=\boxed{\frac{2400+500x}{600(800+x)}}$

Concentration of Green candies in the mixture=$\frac{C_{AG}+C_{BG}}{2}=\frac{1}{2}(\frac{600}{600+x}+\frac{600x}{800(600+x)})=\frac{1}{2}(\frac{4800+600x}{600(800+x)})=\boxed{\frac{2400+300x}{600(800+x)}}$

If you compare the concentrations of both the candies in the last mixture, you can conclude that Red candies are more concentrated than Green candies

$\therefore$ Red candies are more likely to be selected in the fourth step. Note by Zakir Husain
1 year ago

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## Comments

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Great! @Zakir Husain. I agree with you but shouldn't you report this as a bug?

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