An urn contains 4 white and 4 black balls. we randomly choose 4 balls. if 2 of them are white and 2 are black, we stop. if not, we replace the balls in the urn and again randomly select 4 balls. this continues until exactly 2 of the 4 chosen are white. what is the probability that we shall make exactly n selections?

The probability that we shall make exactly n selections is .

Step-by-step explanation:

It is given that an urn contains 4 white and 4 black balls and we randomly choose 4 balls. If 2 of them are white and 2 are black, we stop.

The total number of ways to select exactly 2 white and 2 black balls.

The total number of ways to select 4 balls from 8 balls is

The probability of selecting exactly 2 white and 2 black balls is

The probability of not selecting exactly 2 white and 2 black balls is

If we not get exactly 2 white and 2 black balls, then we replace the balls in the urn and again randomly select 4 balls.

The probability that we shall make exactly n selections is

Therefore the probability that we shall make exactly n selections is .

Step-by-step explanation: You have to substitute the numbers in for x & y

(0, -5): YES

3x - 4y - 8 = 12

3(0) - 4(-5) - 8 = 12

0 + 20 - 8 = 12

20 - 8 = 12

12 = 12

(4, -2): YES

3x - 4y - 8 = 12

3(4) - 4(-2) - 8 = 12

12 + 8 - 8 = 12

20 - 8 = 12

12 = 12

(8, 2): NO

3x - 4y - 8 = 12

3(8) - 4(2) = 12

24 - 8 = 12

16 = 12

(-16, -17): YES

3x - 4y - 8 = 12

3(-16) - 4(-17) - 8 = 12

-48 + 68 - 8 = 12

20 - 8 = 12

12 = 12

(-1, -8): NO

3x - 4y - 8 = 12

3(-1) - 4(-8) = 12

-3 + 32 = 12

29 = 12

(-40, -34): NO

3x - 4y - 8 = 12

3(-40) - 4(-34) - 8 = 12

-120 + 136 - 8 = 12

16 - 8 = 12

8 = 12

Hope this help you!!! :)