there are 6 orange, 5 pink, and 3 white marbles. marbles not returned. P(first marble orange, second marble not white, third marble not orange. I thought but wrong.6/14*10/13*8/12=480/2184
To calculate the probability of drawing an orange marble first, a non-white marble second, and a non-orange marble third, you need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Calculate the number of favorable outcomes - drawing an orange marble first.
There are 6 orange marbles out of a total of 14 marbles, therefore, the probability of drawing an orange marble first is 6/14.
Step 2: Calculate the number of favorable outcomes - drawing a non-white marble second.
After drawing an orange marble (favorable outcome), there are now 13 marbles left, out of which there are 10 non-white marbles (5 pink + 3 white). Therefore, the probability of drawing a non-white marble second is 10/13.
Step 3: Calculate the number of favorable outcomes - drawing a non-orange marble third.
After drawing an orange marble (favorable outcome) and a non-white marble (favorable outcome), there are now 12 marbles left, out of which there are 8 non-orange marbles (5 pink + 3 white). Therefore, the probability of drawing a non-orange marble third is 8/12.
Step 4: Multiply the probabilities together to get the overall probability.
To find the overall probability, you multiply the individual probabilities calculated in Steps 1, 2, and 3 together:
(6/14) * (10/13) * (8/12) = 480/2184
So, the correct calculation of the probability is 480/2184, which can be simplified if needed.