# One urn contains 4 green, 6 red balls. The other has 16 green and x red. One ball at a time is pulled

**One urn contains 4 green, 6 red balls. The other has 16 green and x red. One ball at a time is pulled out of the urns. The probability of drawing balls of the same color is 0.58. Find x.**

The first urn contains 4 + 6 = 10 balls.

The probability of getting a red ball from the first urn is p1 = 6/10 = 0.6.

The probability of getting a green ball from the first urn is p2 = 4/10 = 0.4.

The probability of getting a red ball from the second urn is p3 = x / (16 + x).

The probability of getting a green ball from the second urn is p4 = 16 / (16 + x).

The appearance of balls from different urns are independent events. The probability of the simultaneous appearance of balls of the same color is equal to the product of the probabilities.

Events such that either a pair of green or a pair of red balls have appeared are incompatible events. The probability of their occurrence is equal to the sum of the probabilities. Then the Probability of pulling balls of the same color:

P = p1 p3 + p2 p4 = 0.6 x / (16 + x) + 0.4 16 / (16 + x);

P = 0.58.

0.6 x / (16 + x) + 0.4 16 / (16 + x) = 0.58;

0.6x + 6.4 = 0.58 (16 + x);

0.6x – 0.58x = 9.28 – 6.4;

0.02x = 2.88.

x = 144.

Answer: In the second urn, x = 144 red balls.