To solve this problem step-by-step:
1. Calculate the Total Number of Purchases:
To find how many total purchases were made in the month, we need to sum up all the numbers in the table.
[tex]\[
\text{Total Purchases} = (41 + 53 + 43) + (73 + 59 + 37) + (89 + 13 + 29) = 437
\][/tex]
2. Calculate the Total Number of Shake Purchases:
Next, we need to sum up only the purchase numbers for shakes across different flavors.
[tex]\[
\text{Shake Purchases} = 53 (\text{Strawberry}) + 59 (\text{Apple}) + 13 (\text{Banana}) = 125
\][/tex]
3. Calculate the Total Number of Strawberry Purchases:
We add up all the purchases related to strawberry products.
[tex]\[
\text{Strawberry Purchases} = 41 (\text{Smoothie}) + 53 (\text{Shake}) + 43 (\text{Ice Cream}) = 137
\][/tex]
4. Calculate the Purchases that are either a Shake or a Strawberry Product:
To determine the number of purchases that are either a shake or a strawberry product, we need to consider the overlap between shakes and strawberry products because strawberry shakes are counted in both categories. Therefore, we subtract the number of strawberry shakes (53) once from the sum of shakes and strawberry products.
[tex]\[
\text{Either Shake or Strawberry Purchases} = 125 (\text{Shakes}) + 137 (\text{Strawberry Products}) - 53 (\text{Strawberry Shakes}) = 209
\][/tex]
5. Calculate the Probability:
Finally, to find the probability that a randomly chosen customer purchased either a shake or a strawberry product, we divide the number of either shake or strawberry purchases by the total number of purchases.
[tex]\[
P(\text{Strawberry or Shake}) = \frac{\text{Either Shake or Strawberry Purchases}}{\text{Total Purchases}} = \frac{209}{437}
\][/tex]
Simplifying this fraction, we find:
[tex]\[
P(\text{Strawberry or Shake}) \approx 0.478
\][/tex]
Thus, the probability that a randomly chosen customer purchased either a shake or a strawberry product is approximately [tex]\( 0.478 \)[/tex] or [tex]\( 47.8\% \)[/tex].
