Question

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?

Answer 1

To find the number of red balls in the second urn, set up a probability equation using the given information. Solve the equation to determine R2.

Step-by-step explanation:

To find the number of red balls in the second urn, we can set up a probability equation based on the information given. Let's use the variables R1 and R2 to represent the number of red balls in the first and second urn respectively.

The probability of drawing two balls of the same color can be calculated as follows:

P(Red in both urns) + P(Blue in both urns)

For the first term, we know that the first urn contains 8 red balls and the second urn contains R2 red balls. So, the probability of drawing two red balls is (8/15) * (R2 / (R2+9)).

For the second term, the probability of drawing two blue balls is (7/15) * (9 / (R2+9)).

We can now set up the equation:

(8/15) * (R2 / (R2+9)) + (7/15) * (9 / (R2+9)) = 151/300

Solving this equation will give us the value of R2, the number of red balls in the second urn.

Answer 2

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
`=P\left ( both\ red\right )+P\left ( both\ blue\right )`

`P=(151)/(300)`

Let Urn 2 contains n red balls

`(151)/(300)=(8)/(15)* (n)/(n+9)+(7)/(15)* (9)/(n+9)`

`(8n+63)/(15* (n+9))=(151)/(300)`

160n+1260=151n+1359

9n=99

n=11

So Urn 2 contains 11 red balls