You have two bags of marbles.
Bag 1 has 5 red and 6 blue marbles.
Bag 2 has 20 green and 5 red marbles.
What is the probability of drawing a red marble out of Bag 2, given that you drew a red marble out of Bag 1?
5/25 = 1/5
It makes no difference what color she drew from Bag 1.
P(R1)=5/11
P(R2)=5/25
Since the drawing of the two bags are independent, we have
P(R1∩R2)=P(R1)*P(R2)
P(R2|R1)=P(R2∩R1)/P(R1)
=P(R1)*P(R2)/P(R1)
=P(R2)
=1/5 as Ms.Sue had it.
To find the probability of drawing a red marble out of Bag 2, given that you drew a red marble out of Bag 1, we can use conditional probability.
Let's denote the events:
A: Drawing a red marble out of Bag 1.
B: Drawing a red marble out of Bag 2.
We want to find P(B|A), the probability of event B occurring given that event A has occurred.
Using conditional probability formula, we have:
P(B|A) = P(A and B) / P(A)
To find P(A and B), we need to calculate the probability of drawing a red marble from both bags simultaneously. Since we know that Bag 1 has 5 red marbles and Bag 2 has 5 red marbles, the probability of drawing a red marble from both bags is (5/11) * (5/25).
Next, we need to calculate P(A), the probability of drawing a red marble out of Bag 1. Since Bag 1 has a total of 11 marbles (5 red + 6 blue), the probability of drawing a red marble from Bag 1 is 5/11.
Now we can substitute the values into the conditional probability formula:
P(B|A) = (5/11) * (5/25) / (5/11)
Simplifying the expression, we get:
P(B|A) = (1/11) * (1/5)
Therefore, the probability of drawing a red marble out of Bag 2, given that you drew a red marble out of Bag 1, is 1/55.