Questions: 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?
P( Strawberry or Shake )=
Transcript text: At an ice cream stand, the purchases for one month are recorded in the table below:
\begin{tabular}{|l|c|c|c|}
\hline & Smoothie & Shake & Ice Cream \\
\hline Strawberry & 41 & 53 & 43 \\
\hline Apple & 73 & 59 & 37 \\
\hline Banana & 89 & 13 & 29 \\
\hline
\end{tabular}
If we choose a customer at random, what is the probability that they have purchased a shake or it is strawberry?
$P($ Strawberry or Shake $)=$ $\square$
Give your answer in simplest form.
Solution
Solution Steps
To find the probability that a randomly chosen customer purchased a shake or it is strawberry, we need to use the principle of inclusion-exclusion. First, calculate the total number of purchases. Then, find the number of purchases that are either a shake or strawberry. Finally, divide the number of favorable outcomes by the total number of purchases to get the probability.
Step 1: Calculate Total Purchases
The total number of purchases is the sum of all the individual purchases for smoothies, shakes, and ice creams across all flavors. This is given by:
The probability that a randomly chosen customer purchased a shake or it is strawberry is given by the ratio of favorable outcomes to the total number of purchases:
\[
P(\text{Strawberry or Shake}) = \frac{\text{Shake or Strawberry}}{\text{Total Purchases}} = \frac{209}{437} \approx 0.4783
\]
Final Answer
The probability that a randomly chosen customer purchased a shake or it is strawberry is: