Every day, Bill buys a lottery ticket. Each ticket has probability 0.25 of winning a prize. After seven days, what is the probability that Bill has won at least one prize?
A) 0.1335
B) 0.9999
C) 0.0001
D) 0.8665

Question

Quizplus · Accepted Answer

The probability that Bill does not win a prize on any given day is 0.75. Therefore, the probability that he does not win a prize on any of the seven days is $(0.75)^7\approx 0.13$. 
Then, the probability that he wins at least one prize is equal to 1 minus the probability that he wins no prizes: $1 - 0.13 = 0.87$. So the answer is D.

Every Day, Bill Buys a Lottery Ticket