Every day, Jorge buys a lottery ticket. Each ticket has a probability of 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.

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