What is the Probability of Getting a Raise at McBurger's Drive-Thru?

In summary, the problem presents a scenario where an employee at McBurger's drive-thru can potentially receive a raise if they serve exactly 20 customers per hour in at least one of the next 3 hours. The probability of this happening is 0.0624, but the question also poses the challenge of considering all 3 hours in the calculation. One approach to solving this is to use the property of probabilities that states that if events are pairwise independent, then the probability of all of them happening is equal to the product of their individual probabilities.
  • #1
rayne1
32
0
Problem:
McBurger’s drive-thru has only one service window and serves an average of 2 customers every 5 minutes. 70% of customers order drinks from the drive-thru.

The manager monitors the employee at the drive-thru for the next 3 hours. He will give the employee a raise if exactly 20 customers are served per hour in at least 1 of these hours. What is the probability that the employee will receive a raise?
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I know the probability that there are exactly 20 customers in the next hour is 0.0624 (rounded), but don't know how to deal with the "at least 1 of these (3) hours" part of the question.
 
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  • #2
Hi rayne!

Hint: what is the chance that none of the 3 hours satisfies the criterion?
 
  • #3
I like Serena said:
Hi rayne!

Hint: what is the chance that none of the 3 hours satisfies the criterion?

Not sure :(
 
  • #4
rayne said:
Not sure :(

A property of the Poisson distribution is that the events in each time interval are independent from each other.

And one of the properties of probabilities is that if $A,B,C$ pairwise independent, then:
$$P(A\wedge B\wedge C) = P(A)P(B)P(C)$$
 
  • #5
I like Serena said:
A property of the Poisson distribution is that the events in each time interval are independent from each other.

And one of the properties of probabilities is that if $A,B,C$ pairwise independent, then:
$$P(A\wedge B\wedge C) = P(A)P(B)P(C)$$

Okay, but I'm still unclear on how to solve it.
 

FAQ: What is the Probability of Getting a Raise at McBurger's Drive-Thru?

What is the Poisson distribution?

The Poisson distribution is a probability distribution that is used to model the number of events that occur in a fixed interval of time or space. It is often used to predict the likelihood of rare events, such as accidents or natural disasters, based on historical data.

How is the Poisson distribution different from other probability distributions?

The Poisson distribution is unique in that it only has one parameter, the rate parameter λ, which represents the average number of events per interval. Other distributions, such as the normal distribution, have multiple parameters that can affect the shape of the distribution.

What is the formula for the Poisson distribution?

The formula for the Poisson distribution is: P(x; λ) = (e^-λ * λ^x) / x!, where x is the number of events, e is the base of the natural logarithm, and x! is the factorial of x.

When should the Poisson distribution be used?

The Poisson distribution is most appropriate when the events being modeled are independent, occur at a constant rate, and are rare. It is commonly used in fields such as insurance, finance, and engineering.

How can the Poisson distribution be applied in real-life situations?

The Poisson distribution can be used to predict the number of accidents or defects in a manufacturing process, the number of customers arriving at a store during a certain time period, or the number of calls received by a call center in a day. It can also be used to analyze data on natural disasters, such as earthquakes or hurricanes, to estimate the likelihood of future events.

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