Two urns each contain green balls and blue balls. Urn I contains 4 green balls and 6 blue balls, and Urn II contains 6 green balls and 2 blue balls. A ball is drawn at random from each urn. What is the probability that both balls are blue?
A. 2/15
B. 3/20
C. 1/10
D. 4/153
To find the probability that both balls drawn are blue, we need to calculate the probability of drawing a blue ball from each urn and multiply those probabilities together.
Let's start with Urn I, which contains 4 green balls and 6 blue balls. The total number of balls in Urn I is 4 + 6 = 10.
The probability of drawing a blue ball from Urn I is given by the number of blue balls (6) divided by the total number of balls (10):
Probability of drawing a blue ball from Urn I = 6/10 = 3/5
Next, let's consider Urn II, which contains 6 green balls and 2 blue balls. The total number of balls in Urn II is 6 + 2 = 8.
The probability of drawing a blue ball from Urn II is given by the number of blue balls (2) divided by the total number of balls (8):
Probability of drawing a blue ball from Urn II = 2/8 = 1/4
Now, we can find the probability that both balls drawn are blue by multiplying the probability of drawing a blue ball from Urn I with the probability of drawing a blue ball from Urn II:
Probability of drawing a blue ball from both urns = (3/5) * (1/4) = 3/20
Therefore, the correct answer is B. 3/20.
Urn 1: 6 blue of 10 total
Urn 2: 2 blue of 8 total
So, P(blue,blue) = 6/10 * 2/8