Question

A cell phone company found that 75% of all customers want text messaging on their Phones, 80% want photo capability, and 65% want both. What is the probability that a customer will want at least one of theses.

Answer 1

Hi
Let's say that 75% of smartphone customers want text messaging; 80% want photo capability; 65% want both. What is the probability that a customer wants photo capability, given that he wants text messaging? 65/75=13/15 or about 86.7%.




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Answer 2

Given,

In a cell phone company;

Percentage of all customers who want text messaging on their phones = 75%

Percentage of all customers who want photo capability on their phones = 80%

Percentage of all customers who want both = 65%

To find,

The probability that a customer chosen at random will want at least one of these.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The probability of occurrence of a favorable event = P (favorable event)

= (Total number of occurrence of the favorable event) / (Total number of occurrence of all possible events)

= (Total number of occurrence of the favorable event) / (Total number of trials)

As per the given question;

The percentage of all customers who want only text messaging on their phones

= Percentage of all customers who want text messaging on their phones - percentage of all customers who want both

= 75% - 65% = 10%

And, the percentage of all customers who want only photo capability on their phones

= Percentage of all customers who want photo capability on their phones - percentage of all customers who want both

= 80% - 65% = 15%

Now,

The percentage of all customers who want at least one of these

= Percentage of all customers who want only text messaging on their phones + percentage of all customers who want only photo capability on their phones + percentage of all customers who want both

= 10% + 15% + 65% = 90%

Now,

The probability that a customer chosen at random will want at least one of these

= (Total number of occurrence of the favorable event) / (Total number of trials)

= (percentage of all customers who want at least one of these)/(total percentage of all the users)

= 90%/100% = 0.9

Hence, the probability that a customer chosen at random will want at least one of these is equal to 0.9.