The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Every day, Jorge buys a lottery ticket. Each ticket has a 0.16 probability of winning a prize. After six days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.
Answer:
The probability that Jorge has won at least one prize after six days is
P(at least 1 win) = 0.6487
Step-by-step explanation:
Every day, Jorge buys a lottery ticket which has a 0.16 chance of winning a prize.
We want to find out the probability that Jorge has won at least one prize after six days.
P(at least 1 win) = 1 - P(not winning for 6 days)
We know that the probability of winning is 0.16 then the probability of not winning is
P(not winning) = 1 - 0.16 = 0.84
For 6 days,
P(not winning for 6 days) = 0.84×0.84×0.84×0.84×0.84×0.84
P(not winning for 6 days) = 0.84⁶
P(not winning for 6 days) = 0.3513
Finally,
P(at least 1 win) = 1 - P(not winning for 6 days)
P(at least 1 win) = 1 - 0.3513
P(at least 1 win) = 0.6487
