Question

Your college roommate orders pizza three days a week on average find the probability that your roommate orders pizza four days a week

Answer 1

The probability of your roommate ordering at least 4 pizzas in a given week can be found using the Poisson distribution with an average rate
`(\( \lambda \))` of 3 pizzas per week. Calculate
`\( P(X \geq 4) = 1 - P(X < 4) \)` using the Poisson probability formula, and round the result to four decimal places.

To solve this problem, we can use the Poisson probability formula since we are dealing with the number of events (pizza orders) in a fixed interval (one week) where events happen with a known constant rate (average of three pizzas per week). The Poisson probability mass function is given by:

`\[ P(X = k) = (e^(-\lambda) \cdot \lambda^k)/(k!) \]`

where:

- \( P(X = k) \) is the probability of observing \( k \) events,

- \( \lambda \) is the average rate of events per interval,

- \( e \) is the mathematical constant approximately equal to 2.71828,

- \( k \) is the actual number of events that occur,

- \( k! \) is the factorial of \( k \).

In this case,
`\( \lambda \)` (the average number of pizzas ordered per week) is 3.

Now, we need to find the probability that your roommate orders at least 4 pizzas in any given week. This is the sum of probabilities for
`\( k \geq 4 \)`:

`\[ P(X \geq 4) = 1 - P(X < 4) \]`

Let's calculate this step by step:

1. Calculate
`\( P(X < 4) \)`:

`\[ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \]\[ P(X = 0) = (e^(-3) \cdot 3^0)/(0!) \]\[ P(X = 1) = (e^(-3) \cdot 3^1)/(1!) \]\[ P(X = 2) = (e^(-3) \cdot 3^2)/(2!) \]\[ P(X = 3) = (e^(-3) \cdot 3^3)/(3!) \]`

2. Calculate
`\( P(X \geq 4) \)`:

`\[ P(X \geq 4) = 1 - P(X < 4) \]`

Round the final result to four decimal places.

Performing these calculations will give you the probability that your roommate orders at least 4 pizzas in any given week.


The probable question can be: Your college roommate orders on average three pizzas each week. Find the probability that your roommate orders at least 4 pizzas in any given week. Round to the nearest ten-thousandth (4 decimal places).