A retailer sells both the Apple iPhone and Google Android cell phones online.

Assume that 80% of the phones the retailer sells online are iPhones and 20% are Androids.

a. Use the steps given in Chapter 3 to find the probability that all of the next four online cell phone purchases are Androids.

b. Find the probability that three of the next four online cell phone purchases are Androids.

c. Let x represent the number of the next four online cell phone purchases are Androids. Explain why x is a binomial random variable.

d. Use the answers to parts a and b to derive a formula for p(x), the probability distribution of the binomial random variable x.

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Steps for Calculating Probabilities of Events Step 1 Step 2 Step 3 Step 4 Define the experiment; that is, describe the process used to make an obser- vation and the type of observation that will be recorded. List the sample points. Assign probabilities to the sample points. Determine the collection of sample points contained in the event of interest. Step 5 Sum the sample point probabilities to get the event probability.