Question

There are seven black marbles and nine white marbles in a bag. What is the approximate probability of drawing two black marbles and then a white marble without replacement?

Answer 1

The probability of drawing two black marbles and then a white marble without replacement is approximately 0.1125.

Step-by-step explanation:

To find the probability of drawing two black marbles and then a white marble without replacement, we need to calculate the probability of each event separately and then multiply them together.

1. The probability of drawing a black marble on the first draw is 7/16 (since there are 7 black marbles out of a total of 16 marbles).
2. After drawing a black marble, there are now 6 black marbles left out of a total of 15 marbles.
3. The probability of drawing a second black marble is therefore 6/15.
4. Finally, after drawing two black marbles, there are now 9 white marbles left out of a total of 14 marbles.
5. The probability of drawing a white marble on the third draw is therefore 9/14.

To find the overall probability, we multiply the probabilities of each event:

(7/16) * (6/15) * (9/14) ≈ 0.1125

Therefore, the approximate probability of drawing two black marbles and then a white marble without replacement is approximately 0.1125.