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

\begin{tabular}{|l|c|c|c|}
\hline
& Phone I & Phone II & Phone III \\
\hline
Mini & 7 & 23 & 31 \\
\hline
Standard & 43 & 41 & 29 \\
\hline
Maximum & 2 & 17 & 13 \\
\hline
\end{tabular}

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.



Answer :

GinnyAnswer
To determine the probability that a randomly chosen customer purchased a mini-sized Phone II, we should follow these steps:

1. Total Number of Customers:
- First, we need to find the total number of all customers who made purchases.
- According to the table, we need to sum up all the purchases across all types and sizes.

Let's summarize the counts:

- For Phone I:
- Mini: 7
- Standard: 43
- Maximum: 2

- For Phone II:
- Mini: 23
- Standard: 41
- Maximum: 17

- For Phone III:
- Mini: 31
- Standard: 29
- Maximum: 13

Adding these values:

[tex]\[ \text{Total customers} = (7+43+2) + (23+41+17) + (31+29+13) \][/tex]

[tex]\[ \text{Total customers} = 52 + 81 + 73 = 206 \][/tex]

2. Number of Customers who Purchased Mini Sized Phone II:
- According to the table, the number of customers who purchased mini-sized Phone II is 23.

3. Probability Calculation:
- The probability [tex]\(P(\text{Mini and Phone II})\)[/tex] is the ratio of customers who purchased the mini-sized Phone II to the total number of customers.

Using the numbers from above:

[tex]\[ P(\text{Mini and Phone II}) = \frac{\text{Number of customers who purchased mini-sized Phone II}}{\text{Total number of customers}} = \frac{23}{206} \][/tex]

This fraction is already in its simplest form because 23 is a prime number and does not divide 206 evenly.

Thus, the probability [tex]\(P(\text{Mini and Phone II})\)[/tex] is:

[tex]\[ P(\text{Mini and Phone II}) = \frac{23}{206} \][/tex]

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