Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has

Question

2 months ago

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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?

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-03-09T10:58:33+03:00

babunello [11.8K]2 months ago

7 0

Answer:

0.76 probability.

Step-by-step explanation:

1 minus the probability of traveling after her birth raised to the fifth power.

1 minus (0.75 multiplied by itself five times)

1 minus (0.24)

=

0.76.

babunello [11.8K] · Answer 2 · 2026-03-09T11:00:03+03:00

The likelihood that at least one trip occurs before Isabella's birth is 0.7627.

Step-by-step explanation:

In this scenario, Isabella has invented a time machine, but she lacks control over where she travels. Each use of the device holds a 0.25 probability of leading her to a time preceding her birth. Over the initial year of trials, she operates her machine 5 times. If we assume every journey has an equal chance of going back in time, we can calculate the odds that at least one of these trips occurs before she was born. Here's the calculation:

The probability of traveling to a time prior to her birth is 0.25.

The chance of not traveling back in time, given that the machine is used 5 times:

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

⇒ $(1-0.25)^5$

⇒ $(0.75)^5$

The probability that at least one trip goes before Isabella's birth is equal to 1 minus the probability of not traveling back to that period:

⇒ $1-(0.75)^5$

⇒ $0.7627$

Consequently, the chance that at least one trip travels before Isabella's birth is 0.7627.