To determine the probability that a randomly chosen customer has purchased a mini sized Phone II, follow these steps:
1. Determine the total number of customers:
Sum up all the customers who have made a purchase, as provided in the table:
[tex]\[
\begin{aligned}
&\text{Mini (Phone I, Phone II, Phone III)}: &7 + 23 + 31 = 61 \\
&\text{Standard (Phone I, Phone II, Phone III)}: &43 + 41 + 29 = 113 \\
&\text{Maximum (Phone I, Phone II, Phone III)}: &2 + 17 + 13 = 32 \\
\end{aligned}
\][/tex]
Adding these totals together gives the overall number of customers:
[tex]\[
61 + 113 + 32 = 206
\][/tex]
So, the total number of customers is 206.
2. Identify the number of customers who purchased a mini sized Phone II:
From the table, the number of customers who purchased a mini sized Phone II is given as:
[tex]\[
23
\][/tex]
3. Calculate the probability:
The probability that a randomly selected customer purchased a mini sized Phone II is the ratio of the number of mini sized Phone II customers to the total number of customers. Hence,
[tex]\[
P(\text{Mini and Phone II}) = \frac{\text{Number of mini sized Phone II customers}}{\text{Total number of customers}} = \frac{23}{206}
\][/tex]
4. Simplified form:
Simplify the fraction [tex]\(\frac{23}{206}\)[/tex]. Note that 23 is a prime number and does not divide evenly into 206, so the fraction is already in its simplest form.
Therefore, the probability that a randomly chosen customer purchased a mini sized Phone II is:
[tex]\[
P(\text{Mini and Phone II}) = \frac{23}{206}
\][/tex]
