McMahon Hall on UW’s North Campus has 11 floors. You observe 7 people entering the elevator on the ground floor. In the absence of additional information, you assume that every person is equally likely to leave the elevator on any floor. What is the probability that on each floor at most 1 person leaves the elevator?

Answers

Answer 1

The probability that on each floor at most 1 person leaves the elevator is approximately 0.00048828125 or 0.0488%.

To determine the probability that on each floor at most 1 person leaves the elevator, we can approach this problem using the concept of independent events.

Let's consider each floor as an independent event where a person can either leave the elevator (event A) or not leave the elevator (event B). We want to find the probability that on each floor, at most 1 person leaves the elevator.

For each floor, there are two possibilities: either 0 person leaves (event B) or 1 person leaves (event A). Since we assume that each person is equally likely to leave the elevator on any floor, the probability of event A (one person leaving) is 1/2, and the probability of event B (no person leaving) is also 1/2.

Since there are 11 floors in total, and each floor's event is independent, we can use the multiplication rule for independent events to find the overall probability.

The probability that on each floor at most 1 person leaves the elevator is:

[tex](1/2)^11[/tex]

This can be calculated as (1/2) multiplied by itself 11 times.

Therefore, the probability is approximately:

0.00048828125

So, the probability that on each floor at most 1 person leaves the elevator is approximately 0.00048828125 or 0.0488%.

To know more about probability refer to-

https://brainly.com/question/30034780

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