To calculate the cumulative probability of selling the different types of donuts given their values, we first need to determine the total number of donuts sold. Then, we can find the probabilities for each specific type of donut and calculate the cumulative probabilities.
From the chart you've provided, we have the following quantities:
- Chocolate Cream filled: 1
- Strawberry: 10
- Kale frosted: 6
- Blueberry: 3
- Cream filled surprise: 5
Adding these quantities together gives:
\(1 + 10 + 6 + 3 + 5 = 25\)
Now, we can calculate the individual probabilities for each type of donut:
- Chocolate Cream filled: \( \frac{1}{25} = 0.04 \)
- Strawberry: \( \frac{10}{25} = 0.40 \)
- Kale frosted: \( \frac{6}{25} = 0.24 \)
- Blueberry: \( \frac{3}{25} = 0.12 \)
- Cream filled surprise: \( \frac{5}{25} = 0.20 \)
Next, we calculate the cumulative probabilities:
- Cumulative probability for Chocolate Cream filled: \(0.04\)
- Cumulative probability for Strawberry: \(0.04 + 0.40 = 0.44\)
- Cumulative probability for Kale frosted: \(0.44 + 0.24 = 0.68\)
- Cumulative probability for Blueberry: \(0.68 + 0.12 = 0.80\)
- Cumulative probability for Cream filled surprise: \(0.80 + 0.20 = 1.00\)
Thus, the cumulative probabilities for each type of donut are:
- Chocolate Cream filled: 0.04
- Strawberry: 0.44
- Kale frosted: 0.68
- Blueberry: 0.80
- Cream filled surprise: 1.00
To summarize, the cumulative probability of selling all five types of donuts, leading up to and including each one, is as follows:
- Cumulative probability for Chocolate Cream filled: 0.04
- Cumulative probability for Strawberry: 0.44
- Cumulative probability for Kale frosted: 0.68
- Cumulative probability for Blueberry: 0.80
- Cumulative probability for Cream filled surprise: 1.00