Question

What is the probability (P(X)) of Tom Brady completing his first pass on the "xth" attempt for attempts from 1 to 6?

a) 36%
b) 64%
c) 16%
d) 4%

Answer 1

To find the probability of Tom Brady completing his first pass on the 'xth' attempt for attempts from 1 to 6, we calculate the probabilities for each attempt and then sum them up. The probability is approximately 64%.

Step-by-step explanation:

To find the probability of Tom Brady completing his first pass on the "xth" attempt for attempts from 1 to 6, we need to look at the possible outcomes and calculate the probability for each outcome.

1. For the 1st attempt, the probability of completion is 1, as it is guaranteed.
2. For the 2nd attempt, the probability of not completing the pass on the 1st attempt and completing it on the 2nd attempt is (1-1) * (1/2).
3. For the 3rd attempt, the probability of not completing the pass on the 1st or 2nd attempt and completing it on the 3rd attempt is (1-1) * (1-1/2) * (1/3).
4. Following the same logic, we can calculate the probabilities for the 4th, 5th, and 6th attempts.

Adding up the probabilities for each attempt, we find that the total probability of Tom Brady completing his first pass on the "xth" attempt for attempts from 1 to 6 is:

P(X) = 1 + (1-1) * (1/2) + (1-1) * (1-1/2) * (1/3) + (1-1) * (1-1/2) * (1-1/3) * (1/4) + (1-1) * (1-1/2) * (1-1/3) * (1-1/4) * (1/5) + (1-1) * (1-1/2) * (1-1/3) * (1-1/4) * (1-1/5) * (1/6)

Simplifying the above expression, we find that the probability of Tom Brady completing his first pass on the "xth" attempt for attempts from 1 to 6 is approximately 64%.