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At a phone store, the purchases for one month are recorded in the table below:

| | Phone I | Phone II | Phone III |
|--------------|---------|----------|-----------|
| Mini | 7 | 23 | 31 |
| Standard | 43 | 41 | 29 |
| Maximum | 2 | 17 | 13 |

If we choose a customer at random, what is the probability that they have purchased a mini-sized Phone II?

[tex]\( P(\text{Mini and Phone II}) = \square \)[/tex]

Give your answer in simplest form.

Sagot :

GinnyAnswer
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.
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