Each of two urns contains green balls and red balls. Urn 1 contains 10 green balls and 14 red balls. Urn 2 contains 4 green balls and 11 red balls. Urn 2 contains 4 green balls and 11 red balls. If a ball is drawn from each urn, what is P(red and red)?

Answer 1

There are several ways to approach this problem, but one possible method is to use the multiplication rule of probability:

P(red and red) = P(red from urn 1) × P(red from urn 2)

To find the probability of drawing a red ball from each urn, we need to use the formula for conditional probability:

P(red from urn 1) = number of red balls in urn 1 / total number of balls in urn 1
P(red from urn 2) = number of red balls in urn 2 / total number of balls in urn 2

Plugging in the values given in the problem, we get:

P(red from urn 1) = 14 / (10 + 14) = 7/12
P(red from urn 2) = 11 / (4 + 11) = 11/15

Therefore,

P(red and red) = (7/12) × (11/15) = 77/180 ≈ 0.4286

Therefore, the probability of drawing a red ball from each urn is approximately 0.4286, or 42.86%.