Respuesta :
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
The probability that Jorge has won at least one prize is 0.6487.
How to calculate the probability?
From the information given, the probability of not winning is given as 0.84.
Therefore, the probability of not winning for 6 days will be:
= 0.84 × 0.84 × 0.84 × 0.84 × 0.84 × 0.84
= 0.3513
Therefore, the probability that Jorge has won at least one prize will be:
= 1 - 0.3513
= 0.6487
In conclusion, the probability that Jorge has won at least one prize is 0.6487.
Learn more about probability on:
https://brainly.com/question/24756209
