Probability of winning a week

Question

I am in an NFL Pickem League. I am 1 of 31 participants. Assuming we all have an equal shot at picking the games correctly what is the probability that I will win at least 1 week out of the 17 total weeks possible?

Answer 1

The probability of winning at least one week is 1 - the probability of losing every week. The probability of winning in any week is 1/31, so the probability of losing is 30/31. Then, the probability of losing all 17 weeks is (30/31)¹⁷, so the probability of winning at least one week is 1 - (30/31)¹⁷

To four decimal places, this is .4273.

Answer 2

Probability of winning in a particular week = 1/31 = 0.03226

number of weeks = 17

x = number of weeks winning

want to compute P(x >= 1) = 1 - P(x=0)

use binomial probability: P(x = 0) = c(17,0) (0.03226)^0(0.9677)^17 = 0.5723

P(X >-1) = 1 - 0.5723 = 0.4277