8. Each of two urns contains green balls and red balls. Urn I contains 10 green balls and 8 red balls. Urn II contains 3 green balls and 10 red balls. If a ball is drawn from each urn, what is P(red and red)?
the two drawings are independent events (they don't affect each other)
p(r & r) = (8/18) * (10/13)
To find the probability of drawing a red ball from each urn, we need to calculate the probability of drawing a red ball from Urn I, and then multiply it by the probability of drawing a red ball from Urn II.
Let's start with Urn I:
- Urn I contains a total of 10 green balls and 8 red balls, so the total number of balls is 10 + 8 = 18.
- The probability of drawing a red ball from Urn I can be calculated as the number of red balls in Urn I divided by the total number of balls in Urn I: P(red from Urn I) = 8 / 18.
Now, let's move on to Urn II:
- Urn II contains a total of 3 green balls and 10 red balls, so the total number of balls is 3 + 10 = 13.
- The probability of drawing a red ball from Urn II can be calculated as the number of red balls in Urn II divided by the total number of balls in Urn II: P(red from Urn II) = 10 / 13.
To find the probability of drawing a red ball from both urns, we multiply the individual probabilities together: P(red and red) = P(red from Urn I) * P(red from Urn II).
So, P(red and red) = (8 / 18) * (10 / 13).
Now, let's calculate this probability:
P(red and red) = (8 / 18) * (10 / 13) = 80 / 234 = 0.34188034 (approximately).
Therefore, the probability of drawing a red ball from each urn (red and red) is approximately 0.34188034.