Question

q 25.) frankies pizza shop offers a special on wednesday nights. you can choose from thick or thin crust, red or white sauce, and sausage, pepperoni, or mushroom topping. the tree diagram and sample space are shown below. a customer randomly chooses a pizza. what is the probability of getting a pizza with thin crust and sausage or pepperoni? express your answer as a fraction in simplest form.

Explanation:

Step1: Calculate total number of pizza combinations

There are 2 crust - types (thin and thick), 2 sauce - types (white and red), and 3 topping - types (sausage, pepperoni, mushroom). The total number of pizza combinations is \(2\times2\times3=12\).

Step2: Calculate number of favorable combinations

For thin - crust pizzas with sausage or pepperoni:

• For thin - crust (1 option), white sauce (1 option), and sausage or pepperoni (2 options), there are \(1\times1\times2 = 2\) combinations.
• For thin - crust (1 option), red sauce (1 option), and sausage or pepperoni (2 options), there are \(1\times1\times2=2\) combinations.

The total number of favorable combinations is \(2 + 2=4\).

Step3: Calculate the probability

The probability \(P\) is the number of favorable outcomes divided by the number of total outcomes. So \(P=\frac{4}{12}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)