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An urn contains eight red and seven blue balls. A second urn contains an unknown number of red balls and nine blue balls. A ball is drawn from each urn at random, and the probability of getting two balls of the same color is 151/300. How many red balls are in the second urn?

Respuesta :

Answer:11 red

Step-by-step explanation:

Given

Urn I contains 8 red and Seven Blue balls

Urn 2 also contains red and  9 blue balls

Probability of selecting two balls of same color[tex]=P\left ( both\ red\right )+P\left ( both\ blue\right )[/tex]

[tex]P=\frac{151}{300}[/tex]

Let Urn  2  contains n red balls

[tex]\frac{151}{300}=\frac{8}{15}\times \frac{n}{n+9}+\frac{7}{15}\times \frac{9}{n+9}[/tex]

[tex]\frac{8n+63}{15\times (n+9)}=\frac{151}{300}[/tex]

160n+1260=151n+1359

9n=99

n=11

So Urn 2 contains 11 red balls

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