The probability that a randomly selected one-topping pizza will not have onions is 17/18.
To calculate the probability that a randomly selected one-topping pizza will not have onions, we first need to determine the total number of possible combinations and then find the number of combinations without onions.
1. **Total Combinations:**
There are three categories to choose from: Sauce, Cheese, and Toppings. In each category, there are different options. To find the total number of combinations, multiply the number of options in each category:
- Total Combinations = (Number of Size options) × (Number of Sauce options) × (Number of Cheese options) × (Number of Toppings options)
- Total Combinations = 3 (Small, Medium, Large) × 2 (Garlic, Marinara) × 3 (Mozzarella, Provolone, Parmesan) × 4 (Pepperoni, Sausage, Ham, Pineapple) = 72 combinations.
2. **Combinations without Onions:**
To find the combinations without onions, consider that onions are one of the topping options, and there are four topping options in total. So, the combinations without onions are 72 (total combinations) - 4 (combinations with onions) = 68 combinations.
3. **Probability Calculation:**
The probability is the number of favorable outcomes (combinations without onions) divided by the total number of possible outcomes.
Probability = (Number of Combinations without Onions) / (Total Combinations) = 68 / 72.
4. **Simplify the Fraction:**
The fraction 68/72 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4.
Probability = 17 / 18.
The question probable maybe:
The menu board at a local pizza restaurant shows all the ordering options. Customers can choose up to one item from each category for a one-topping pizza.
Size Sauce Cheese Toppings
________________________________________
Small Garlic Mozzarella Pepperoni
Medium Marinara Provolone Sausage
Large Parmesan Ham
Pineapple
Onions
Peppers
________________________________________
What is the probability that a randomly selected one-topping pizza will not have onions on it? Express your answer as a simplified fraction.