A bag contains two blue, three purple, four yellow, two red, three green and one orange marbles.p> What is the conditional probability that, without replacement, the second marble is purple given that the first marble is green?
0.2142
To find the conditional probability that the second marble is purple given that the first marble is green, we need to find two probabilities:
1. The probability of drawing a green marble first.
2. The probability of drawing a purple marble second, given that a green marble was drawn first.
Let's calculate these probabilities step by step:
Step 1: Calculating the probability of drawing a green marble first.
The total number of marbles in the bag is 2 blue + 3 purple + 4 yellow + 2 red + 3 green + 1 orange = 15 marbles.
The number of green marbles in the bag is 3.
Therefore, the probability of drawing a green marble first is 3/15, which simplifies to 1/5.
Step 2: Calculating the probability of drawing a purple marble second, given that a green marble was drawn first.
After drawing a green marble, there are now 14 remaining marbles in the bag.
The number of purple marbles in the bag is still 3.
Therefore, the probability of drawing a purple marble second, given that a green marble was drawn first, is 3/14.
So, the conditional probability that the second marble is purple, given that the first marble is green, is 3/14.
To summarize:
P(second marble is purple | first marble is green) = 3/14