A bag contains 6 purple marbles and 4 green marbles and 3 blue marbles. A marble is drawn at random and is replaced. Then a second marble is drawn. What is the probability that both marbles are purple?
6/13
To find the probability of drawing two purple marbles, we can use the concept of independent events. Since the first marble is replaced, the probability of drawing a purple marble on the second draw is the same as the first draw.
Step 1: Find the probability of drawing a purple marble on the first draw:
The bag contains a total of 6 + 4 + 3 = 13 marbles, and 6 of them are purple. So, the probability of drawing a purple marble on the first draw is 6/13.
Step 2: Find the probability of drawing a purple marble on the second draw:
Since the first marble drawn is replaced, the probability of drawing a purple marble on the second draw is also 6/13.
Step 3: Multiply the probabilities of the two draws:
Since the two draws are independent events, we multiply the probabilities of each draw to find the probability of both events happening. So, the probability of drawing two purple marbles is (6/13) * (6/13) = 36/169.
Therefore, the probability of drawing two purple marbles is 36/169.
To find the probability of drawing two purple marbles, we need to find the probability of drawing a purple marble on the first draw and then drawing another purple marble on the second draw.
The probability of drawing a purple marble on the first draw can be calculated by dividing the number of purple marbles (6) by the total number of marbles (6 purple + 4 green + 3 blue = 13 marbles).
So, the probability of drawing a purple marble on the first draw is 6/13.
Since we're replacing the first marble back into the bag, the probability of drawing a purple marble on the second draw is the same as the probability of drawing a purple marble on the first draw, which is 6/13.
To find the probability of both events happening (drawing a purple marble on the first draw and a purple marble on the second draw), we multiply the probabilities:
(6/13) * (6/13) = 36/169
Therefore, the probability that both marbles drawn are purple is 36/169.
Since you are returning the marble the second event is not dependent
on the first.
Prob(2 purple) = (6/13)(6/13) = ...