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)?
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%.