Two urns each contain yellow balls and black balls. Urn 1 contains 2 yellow balls and 6 black balls. urn2 contains 2 yellow balls and 5 black balls. A ball is drawn from each urn. What is the probability that both balls are yellow?
Please show me how do do this math problem.
The "events" of drawing a yellow ball from each urn are independent, so you multiply the probabilities of each.
They are 2/8 = 1/4 for the first urn and 2/7 for the second urn. The "joint probability" is therefore
(1/4)*(2/7)= 2/28 = 1/14
To solve this problem, we need to find the probability that a yellow ball is drawn from both urns.
Step 1: Find the probability of drawing a yellow ball from Urn 1.
Urn 1 has a total of 2 yellow balls out of 8 total balls. Therefore, the probability of drawing a yellow ball from Urn 1 is 2/8 or 1/4.
Step 2: Find the probability of drawing a yellow ball from Urn 2.
Urn 2 has a total of 2 yellow balls out of 7 total balls. Therefore, the probability of drawing a yellow ball from Urn 2 is 2/7.
Step 3: Multiply the probabilities from steps 1 and 2 to get the probability of drawing a yellow ball from both urns.
Probability of drawing a yellow ball from both urns = (1/4) * (2/7) = 2/28 or 1/14.
Therefore, the probability that both balls drawn are yellow is 1/14.
To find the probability of both balls being yellow, we first need to determine the probability of drawing a yellow ball from each urn separately and then multiply those probabilities together.
Let's start with Urn 1. There are a total of 2 yellow balls and 6 black balls, so the probability of drawing a yellow ball from Urn 1 is 2/8 (2 yellow balls divided by the total number of balls).
Next, we consider Urn 2. Similar to Urn 1, there are 2 yellow balls and 5 black balls, so the probability of drawing a yellow ball from Urn 2 is 2/7 (2 yellow balls divided by the total number of balls).
To find the probability of both events happening, we multiply the probabilities together:
P(both balls are yellow) = P(yellow from Urn 1) * P(yellow from Urn 2)
= (2/8) * (2/7)
Now, we can calculate this:
(2/8) * (2/7) = 4/56
Simplifying the fraction, 4/56 can be reduced to 1/14.
Therefore, the probability that both balls drawn are yellow is 1/14 or approximately 0.0714.
Note: It's worth mentioning that when drawing balls without replacement, the probability changes after each draw. In this case, we assumed that the ball drawn from Urn 1 is not returned before drawing from Urn 2.