A dog completes a trick 8 out of 20 times. What is the probability the dog completes a trick at most 6 times
To find the probability that the dog completes a trick at most 6 times, we need to find the probability that the dog completes the trick 0, 1, 2, 3, 4, 5, or 6 times.
The probability of completing the trick 0 times is: 1 - 8/20 = 12/20.
The probability of completing the trick 1 time is: 8/20.
The probability of completing the trick 2 times is: (8/20) * (7/19).
The probability of completing the trick 3 times is: (8/20) * (7/19) * (6/18).
The probability of completing the trick 4 times is: (8/20) * (7/19) * (6/18) * (5/17).
The probability of completing the trick 5 times is: (8/20) * (7/19) * (6/18) * (5/17) * (4/16).
The probability of completing the trick 6 times is: (8/20) * (7/19) * (6/18) * (5/17) * (4/16) * (3/15).
Adding up these probabilities, we find that the probability of the dog completing a trick at most 6 times is:
(12/20) + (8/20) + (8/20) * (7/19) + (8/20) * (7/19) * (6/18) + (8/20) * (7/19) * (6/18) * (5/17) + (8/20) * (7/19) * (6/18) * (5/17) * (4/16) + (8/20) * (7/19) * (6/18) * (5/17) * (4/16) * (3/15).
Evaluating this expression yields the final answer.