A bag has 4 green marbles, 3 red marbles, and 3 yellow marbles. What is the probability that you pick a yellow marble, do not replace it, and pick another yellow marble?
What is (3/10)(2/9) ?
To find the probability of picking a yellow marble, not replacing it, and then picking another yellow marble, we need to follow a few steps.
Step 1: Determine the total number of marbles in the bag.
In this case, the bag has a total of 4 green marbles + 3 red marbles + 3 yellow marbles = 10 marbles.
Step 2: Calculate the probability of picking a yellow marble on the first draw.
The probability of picking a yellow marble on the first draw is the number of yellow marbles divided by the total number of marbles in the bag. So, the probability is 3 yellow marbles / 10 total marbles = 3/10.
Step 3: Calculate the probability of picking another yellow marble without replacement.
After removing one yellow marble from the bag, we are left with 2 yellow marbles and 9 total marbles. Therefore, the probability of picking another yellow marble without replacement is 2 yellow marbles / 9 total marbles = 2/9.
Step 4: Multiply the probabilities of the two events.
To find the probability of both events happening together, we multiply the probabilities of each event. So, the probability of picking a yellow marble, not replacing it, and then picking another yellow marble is (3/10) * (2/9) = 6/90 = 1/15.
Therefore, the probability of picking a yellow marble, not replacing it, and then picking another yellow marble is 1/15.