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 answer is 18/31
To calculate the probability of drawing a red ball from each urn (P(red and red)), we can multiply the probabilities of drawing a red ball from each urn.
The probability of drawing a red ball from Urn I is calculated as the ratio of red balls to the total number of balls in Urn I. In this case, there are 8 red balls out of a total of 10 green balls plus 8 red balls in Urn I.
So, the probability of drawing a red ball from Urn I is 8/(10+8) = 8/18 = 4/9.
Similarly, the probability of drawing a red ball from Urn II is the ratio of red balls to the total number of balls in Urn II, which is 10/(3+10) = 10/13.
To find the probability of both events occurring (drawing a red ball from Urn I and Urn II), we multiply these individual probabilities together:
P(red and red) = P(red in Urn I) x P(red in Urn II)
= (4/9) x (10/13)
= 40/117.
However, this is not the same as the answer you provided (18/31). It's possible that there is an error in the calculations or some misunderstanding in the problem statement. Please check again and let me know if there are any additional details.
To find the probability of drawing a red ball from each urn, we need to calculate the individual probabilities and then multiply them together.
Let's start by calculating the probability of drawing a red ball from Urn I.
Urn I contains a total of 10 + 8 = 18 balls. So, the probability of drawing a red ball from Urn I is 8/18.
Next, let's calculate the probability of drawing a red ball from Urn II.
Urn II contains a total of 3 + 10 = 13 balls. So, the probability of drawing a red ball from Urn II is 10/13.
To find the probability of drawing a red ball from both urns, we multiply the probabilities of drawing a red ball from each urn:
P(red and red) = P(red from Urn I) * P(red from Urn II)
= (8/18) * (10/13)
= 80/234
= 40/117
Therefore, the probability of drawing a red ball from each urn is 40/117, which is not equal to 18/31.
It's possible that there might be a mistake in the answer, or perhaps some additional information is missing.
I disagree. How did you arrive at that answer?
Remember, you multiply probabilities for independent events.