At an ice cream stand, the purchases for one month are recorded in the table below:

| | Smoothie | Shake | Ice Cream |
|----------------|----------|-------|-----------|
| Strawberry | 41 | 53 | 43 |
| Apple | 73 | 59 | 37 |
| Banana | 89 | 13 | 29 |

If we choose a customer at random, what is the probability that they have purchased a shake or it is strawberry?

[tex]$ P(\text{Strawberry or Shake}) = \underline{\hspace{1cm}} $[/tex]

Give your answer in simplest form.

First, let us examine the data provided in the table to understand the problem. We have the following purchases for one month at an ice cream stand:

[tex]\[ \begin{array}{|l|c|c|c|} \hline & \text{Smoothie} & \text{Shake} & \text{Ice Cream} \\ \hline \text{Strawberry} & 41 & 53 & 43 \\ \hline \text{Apple} & 73 & 59 & 37 \\ \hline \text{Banana} & 89 & 13 & 29 \\ \hline \end{array} \][/tex]

### Step-by-Step Solution:

#### Step 1: Calculate the Total Number of Entries
To find the total number of customers who made a purchase, we sum all the values in the table:

[tex]\[ 41 + 73 + 89 + 53 + 59 + 13 + 43 + 37 + 29 = 437 \][/tex]

So, the total number of entries is [tex]$ 437 $[/tex].

#### Step 2: Calculate the Number of Customers Who Bought a Shake
We add the values under the "Shake" column:

[tex]\[ 53 \, (\text{Strawberry}) + 59 \, (\text{Apple}) + 13 \, (\text{Banana}) = 125 \][/tex]

So, the number of customers who bought a shake is [tex]$ 125 $[/tex].

#### Step 3: Calculate the Number of Customers Who Bought Strawberry Items
We add the values under the "Strawberry" row:

[tex]\[ 41 \, (\text{Smoothie}) + 53 \, (\text{Shake}) + 43 \, (\text{Ice Cream}) = 137 \][/tex]

So, the number of customers who bought strawberry items is [tex]$ 137 $[/tex].

#### Step 4: Avoid Double-Counting Customers Who Bought Both Strawberry and Shake
To avoid double-counting, we identify the customers who bought a strawberry shake.

[tex]\[ 53 \][/tex]

So, the number of customers who bought both strawberry and shake is [tex]$ 53 $[/tex].

#### Step 5: Calculate the Number of Customers Who Bought a Shake or It is Strawberry
We use the principle of inclusion and exclusion to avoid double-counting:

[tex]\[ \text{Shake or Strawberry} = \text{Shake Customers} + \text{Strawberry Customers} - \text{Customers who bought both Shake and Strawberry} \][/tex]

[tex]\[ \text{Shake or Strawberry} = 125 + 137 - 53 = 209 \][/tex]

#### Step 6: Calculate the Probability in Simplest Form
The probability is given by the ratio of the number of customers who bought a shake or it is strawberry to the total number of customers:

[tex]\[ P(\text{Shake or Strawberry}) = \frac{209}{437} \][/tex]

#### Step 7: Express the Probability as a Decimal
This fraction simplifies to approximately:

[tex]\[ \frac{209}{437} \approx 0.47826 \][/tex]

Thus, the probability that a randomly chosen customer has purchased a shake or it is strawberry is approximately [tex]$0.47826$[/tex] or 47.826%.

So, the final answer is:
[tex]\[ P (\text{Strawberry or Shake}) = \frac{209}{437} \][/tex]