Let's solve the given problem step-by-step to find the probability that a randomly chosen customer purchased a mini-sized Phone II.
### Step 1: Identify the specific event
We are looking for the probability that a randomly chosen customer purchased a mini-sized Phone II. According to the table, the number of purchases for mini-sized Phone II is:
[tex]\[ 23 \][/tex]
### Step 2: Calculate the total number of purchases
To find the total number of purchases, we sum up all the numbers in the table:
[tex]\[
7 + 23 + 31 + 43 + 41 + 29 + 2 + 17 + 13
\][/tex]
Let's break it down:
[tex]\[
7 + 23 = 30 \\
30 + 31 = 61 \\
61 + 43 = 104 \\
104 + 41 = 145 \\
145 + 29 = 174 \\
174 + 2 = 176 \\
176 + 17 = 193 \\
193 + 13 = 206
\][/tex]
Thus, the total number of purchases is:
[tex]\[
206
\][/tex]
### Step 3: Compute the probability
The probability of choosing a customer who purchased a mini-sized Phone II is calculated by dividing the number of mini Phone II purchases by the total number of purchases.
[tex]\[
P (\text{Mini and Phone II}) = \frac{\text{Number of mini Phone II purchases}}{\text{Total number of purchases}} = \frac{23}{206}
\][/tex]
Simplifying the fraction:
[tex]\[
\frac{23}{206} = 0.11165048543689321
\][/tex]
Thus, the probability that a randomly chosen customer purchased a mini-sized Phone II is approximately [tex]\( 0.112 \)[/tex] when rounded to three decimal places, but it's best to leave it in its simplest fractional form, [tex]\(\frac{23}{206}\)[/tex], if exact form is required.
Therefore,
[tex]\[
P (\text{Mini and Phone II}) = \frac{23}{206}
\][/tex]
This is the probability in simplest form.
