Mathematics, 28.03.2020 22:57 jesusalmaraz

Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has a 0.250.250, point, 25 probability of traveling to a time before she was born. During the first year of testing, Isabella uses her machine 555 times. Assuming that each trip is equally likely to travel before Isabella was born, what is the probability that at least one trip will travel before Isabella was born?

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Answer from: SunsetPrincess

The probability of not travelling any time before she was born, the time machine is used 5 times is 1.76.

The probability that at least one trip will travel before she was born is 0.7627.

Given that,

She has a 0.25, 0.250, point 25 probability of traveling to a time before she was born.

During the first year of testing, she uses her machine 5 times.

We have to determine,

What is the probability that at least one trip will travel before she was born.

According to the question,

She have probability of traveling to a time before she was born of 0.25.

Probability of not travelling any time before she was born, is written time machine is used 5 times.

$= (1-0.25)\times(1-0.25)\times (1-0.25)\times(1-0.25)\times (1-0.25)\\\\= (1-0.25)^{5} \\\\= (0.75)^{5} \\\\= 1.762$

Therefore, The probability of not travelling any time before she was born, the time machine is used 5 times is 1.76.

Probability that at least one trip will travel before she was born is equal to 1 - Probability of not travelling any time before she was born.

$= 1-(0.75)^{5}\\\\= 1 - 1.7627\\\\= 0.7627$

Therefore, The probability that at least one trip will travel before she was born is 0.7627.

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Answer from: ajaymatthew15

the probability that at least one trip will travel before Isabella was born is 0.7627

Step-by-step explanation:

Here we have , Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has a 0.25 point, probability of traveling to a time before she was born. During the first year of testing, Isabella uses her machine 5 times. Assuming that each trip is equally likely to travel before Isabella was born, We need to find what is the probability that at least one trip will travel before Isabella was born . Let's find out:

Isabella have probability of traveling to a time before she was born of 0.25

Probability of not travelling any time before Isabella was born , given that time machine is used 5 times :

⇒ (1-0.25)(1-0.25)(1-0.25)(1-0.25)(1-0.25)

⇒ (1-0.25)^5

⇒ (0.75)^5

Probability that at least one trip will travel before Isabella was born is equivalent to 1 - Probability of not travelling any time before Isabella was born i.e.

⇒ 1-(0.75)^5

⇒ 0.7627

Therefore , the probability that at least one trip will travel before Isabella was born is 0.7627

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