Answer:
43.46% probability that the person will need to wait at least 9 minutes total
Step-by-step explanation:
To solve this question, we need to understand conditional probability and the exponential distribution.
Conditional probability:
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
Expontial distribution:
The exponential probability distribution, with mean m, is described by the following equation:
In which is the decay parameter.
The probability that x is lower or equal to a is given by:
Which has the following solution:
The probability of finding a value higher than x is:
In this question:
Event A: Waited at least 4 minutes.
Event B: Waiting at least 9 minutes.
The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes.
This means that
Probability of waiting at least 4 minutes.
Intersection:
The intersection between a waiting time of at least 4 minutes and a waiting time of at list 9 minutes is a waiting time of 9 minutes. So
What is the probability that the person will need to wait at least 9 minutes total
43.46% probability that the person will need to wait at least 9 minutes total
