Each of two urns contains green balls and red balls. Urn I contains 8 green balls and 12 red balls. Urns II contains 5 green balls and 8 red balls. If a ball is drawn from each urn, what is P(red and red)
The probability of drawing red from urn I is 12/20 = 3/5.
The probability of drawing red from urn II is 8/13.
To find the probability of both events happening (red and red), we multiply their probabilities:
P(red and red) = (3/5) x (8/13)
Simplifying, we get:
P(red and red) = 24/65
To find the probability of drawing a red ball from each urn, we need to find the probability of drawing a red ball from Urn I and a red ball from Urn II, and then multiply them together.
First, let's find the probability of drawing a red ball from Urn I. Urn I contains a total of 8 + 12 = 20 balls. Since there are 12 red balls in Urn I, the probability of drawing a red ball from Urn I is 12/20 = 0.6.
Next, let's find the probability of drawing a red ball from Urn II. Urn II contains a total of 5 + 8 = 13 balls. Since there are 8 red balls in Urn II, the probability of drawing a red ball from Urn II is 8/13 ≈ 0.615.
To find the probability of drawing a red ball from each urn, we multiply the probabilities together:
P(red and red) = P(red from Urn I) * P(red from Urn II)
= 0.6 * 0.615
≈ 0.369
Therefore, the probability of drawing a red ball from each urn is approximately 0.369.