There are 6 blue,5 gray,and 5 green marbles in a hat.you pick 4 marbles from the hat. marbles are not returned after they have been drawn.P(the first marble is gray, the second marble is gray, the third marble is not gray, and the fourth marble is not gray)so,? 5*4*11*10/16*15*14*13
To calculate the probability of getting a specific sequence of marble draws, we need to consider the number of favorable outcomes (the desired sequence of draws) and the total number of possible outcomes.
First, let's find the number of favorable outcomes:
1. Picking the first gray marble: There are 5 gray marbles, so the probability of picking a gray marble is 5/16 (since there are 16 total marbles).
2. Picking the second gray marble: After the first gray marble is drawn, there are 4 gray marbles left. The probability of picking a second gray marble is 4/15 (since there are only 15 marbles left).
3. Picking a non-gray marble as the third one: After the first two gray marbles are drawn, there are 11 non-gray marbles left (6 blue and 5 green). The probability of picking a non-gray marble as the third one is 11/14 (since there are only 14 marbles left).
4. Picking a non-gray marble as the fourth one: After the first three draws, there are 10 non-gray marbles left. The probability of picking a non-gray marble as the fourth one is 10/13 (since there are only 13 marbles left).
Now, let's find the total number of possible outcomes:
When drawing 4 marbles without replacement, the total number of possible outcomes is given by the product of the number of marbles available for each draw:
16 * 15 * 14 * 13
Therefore, the probability of getting the specified sequence is:
(5/16) * (4/15) * (11/14) * (10/13)
Simplifying this expression gives the final answer.