Question
A pizza shop offers a special on a 2-topping pizza from a list of four items. The chart below shows all possi Pizza Topping 1 If a person randomly chooses the items on his pizza, what is the probability he chooses a pizza with sausage (1)/(16) (1)/(8) (1)/(4) (1)/(2)
Solution
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NadiaMaster · Tutor for 5 years
Answer
### \(\frac{7}{16}\)
Explain
## Step 1: Determine Total Possible Combinations<br />### The table shows all possible combinations of two toppings from a list of four items: Pepperoni, Ham, Sausage, and Olives. Since each topping can pair with itself or any other topping, the total number of combinations is \(4 \times 4 = 16\).<br /><br />## Step 2: Identify Combinations Involving Sausage<br />### We need to count how many of these combinations include Sausage. From the table:<br />- Sausage & Pepperoni: "SP"<br />- Sausage & Ham: "SH"<br />- Sausage & Sausage: "SS"<br />- Sausage & Olives: "SO"<br />- Pepperoni & Sausage: "PS"<br />- Ham & Sausage: "HS"<br />- Olives & Sausage: "OS"<br /><br />### There are 7 combinations involving Sausage.<br /><br />## Step 3: Calculate Probability<br />### The probability of choosing a pizza with Sausage is the number of favorable outcomes (combinations involving Sausage) divided by the total number of possible combinations.<br />\[<br />\text{Probability} = \frac{\text{Number of combinations with Sausage}}{\text{Total combinations}} = \frac{7}{16}<br />\]
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