Problem 1: Papa John’s Pizza offers the following toppings for cheese pizzas:

3 Meat Toppings: Ham, Pepperoni, Canadian Bacon

4 Vegetable Toppings: Mushroom, Green Pepper, Garlic, Tomato.

1. John wants to list all the items on the menu. How many ways can he arrange these 7 items on a menu?
2. How many possible 3-topping pizzas could you order from Papa John’s
3. If you randomly choose a 3-topping pizza, what’s the probability that it will contain all vegetable toppings
4. If you randomly choose a 3-topping pizza, what is the probability that it will contain more vegetable than meat topping?

Problem 2: More pizza: You order from two pizza stores A and B. The probability that Store A delivers in 30 minutes or less is 0.95, and the probability that Store B delivers in under 30 minutes is 0.90. Assuming the two pizza companies deliver pizza independently, find the following probability:

1. Both pizzas arrive in 30 minutes or less.
2. Neither pizza is delivered in less than 30 minutes:
3. At least one of the pizzas is delivered on time.

Problem 3: The Candy Company has three machines in operation producing its specialty candies. Machine A produces 8% defective candies, Machine B produces 6% defective candies, and Machine C produces 5% defective candies. Machine A produces 20% of the candies, Machine B produces 30% of the candies and Machine C produces 50% of the candies.

1. If you selected a candy at random, what is the probability that it is defective?
2. Given a candy is defective, what is the probability that it comes from machine B?

Problem 4: Based on recent records, the manager of a car painting center has determined that following probability distribution for \(X\), the number of customers per day.

1. If the center has the capacity to serve two customers per day, what’s the probability that one or more customers will be turned away any given day?
2. By how much must the capacity be increased so the probability of turning a customer away is no more than 0.10?
3. Find the cumulative distribution function \(F(x)\).

Problem 5: If the probability density function of \(X\) is

\end{aligned} \right.\]

1. Determine the value of \(c\).
2. Find \(\Pr \left( X<\frac{1}{4} \right)\).
3. Find \(\Pr (X>1)\).

Problem 6: If the joint density of \(X\) and \(Y\) is given by

\end{aligned} \right.\]

1. Find the marginal distribution function of \(X\).
2. Find the marginal distribution of \(Y\).
3. Find the conditional density function given \(X=\frac{1}{4}\)

Price: $12.51

Solution: The downloadable solution consists of 6 pages, 651 words.
Deliverable: Word Document