Two urns both contain green balls and red balls. Urn I contains 6 green balls and 4 red balls and Urn I contains 8 green balls and 7 red balls. A ball is drawn from each urn. What is the probability that both balls are red?
The probability of drawing a red ball from Urn I is 4/10 = 2/5. The probability of drawing a red ball from Urn II is 7/15.
The probability of both events happening (drawing a red ball from both urns) is equal to the product of their probabilities:
P(both red) = P(red from Urn I) × P(red from Urn II)
P(both red) = (2/5) × (7/15)
P(both red) = 14/75
Therefore, the probability of drawing two red balls is 14/75.
To find the probability that both balls drawn are red, we need to find the product of the probability of drawing a red ball from each urn.
Urn I contains 6 green balls and 4 red balls. The probability of drawing a red ball from Urn I is:
P(Red from Urn I) = Number of red balls in Urn I / Total number of balls in Urn I
P(Red from Urn I) = 4 / (6 + 4)
P(Red from Urn I) = 4/10
P(Red from Urn I) = 2/5
Similarly, Urn II contains 8 green balls and 7 red balls. The probability of drawing a red ball from Urn II is:
P(Red from Urn II) = Number of red balls in Urn II / Total number of balls in Urn II
P(Red from Urn II) = 7 / (8 + 7)
P(Red from Urn II) = 7/15
Now, to find the probability that both balls drawn are red, we need to find the product of these two probabilities:
P(Both red) = P(Red from Urn I) × P(Red from Urn II)
P(Both red) = (2/5) × (7/15)
P(Both red) = 14/75
Therefore, the probability that both balls drawn are red is 14/75.