In this problem, we will analyze basic probability concepts. For each calculation provide your answer and explain how you made the calculation. You may show a formula, an Excel formula, a table, or describe textually. Your goal is to explain your approach clearly and succinctly.

Do the following:

Recently Apple announced the new iPhone 13 Pro, and iPhone 13 Pro Max. They are offered with a number of options including

o Four Colors: Graphite, Gold, Silver, and Sierra Blue

o Four Capacities: 128 GB, 256GB and 512 GB, and 1TB

o 4 Carriers (AT&T, Sprint, T-Mobile. Verizon)

At the same time, they announced the iPhone 13 and iPhone 13 Mini with the following options:

o Five Colors: Red, Starlight, Midnight, Blue, and Pink

o Three Capacities: 128GB, 256GB and 512GB

o 4 Carriers Based on this information calculate the total number of new configurations available.

Calculate the total number of configurations available ignoring the carrier.

A retailer wants to display 5 phones in an interactive display.

o Calculate the total number of ways the retailer can select phone configurations for the display, ignoring carrier and order.

o Recalculate the number of ways the phones can be displayed if order of display matters.

Assume that a battery defect effects 1% of the phones. Calculate the following probabilities for the 5 display phones:

o None of the phones have the defect

o Exactly one of the phones has the defect.

o The set of 5 phones has 1 or less defects.

Now assume the retailer wants to stock 25 phones of each Pro configuration and 30 of each non-Pro configuration for each of the 4 carriers. Based on this population, calculate the following:

o The total number of phones to stock

o The probability a randomly selected iPhone is Silver.

o The probability a randomly selected iPhone is Red.

o The probability a randomly selected iPhone is an iPhone 13 Pro given that it is Gold.

o The probability a randomly selected iPhone is an iPhone 13 Mini given that it is has a 512 GB capacity