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A pizza shop offers a special on a 2-topping pizza from a list of four items. The chart below shows all possible pizza combinat If a person randomly chooses the items on his pizza, what is the probability he chooses a pizza with sausage and pepperoni? (1)/(16) (1)/(8) (1)/(4) (1)/(2)

Question

A pizza shop offers a special on a 2-topping pizza from a list of four items. The chart below shows all possible pizza combinat If a person randomly chooses the items on his pizza, what is the probability he chooses a pizza with sausage and pepperoni? (1)/(16) (1)/(8) (1)/(4) (1)/(2)

A pizza shop offers a special on a 2-topping pizza from a list of four items. The chart below shows all possible pizza combinat
If a person randomly chooses the items on his pizza, what is the probability he chooses a pizza with sausage and pepperoni?
 (1)/(16) 
 (1)/(8) 
 (1)/(4) 
 (1)/(2)

Solution

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KieraMaster · Tutor for 5 years

Answer

### \( \frac{1}{16} \)

Explain

## Step 1: Identify the Total Number of Combinations<br />### The table shows all possible combinations of two toppings from a list of four items (Pepperoni, Ham, Sausage, Olives). Each combination is represented by a unique code. There are 4 rows and 4 columns of combinations, making a total of $4 \times 4 = 16$ possible combinations.<br /><br />## Step 2: Identify the Desired Combination<br />### We need to find the probability of choosing a pizza with both sausage and pepperoni. From the table, the code for this combination is "SP" (Sausage + Pepperoni).<br /><br />## Step 3: Count the Occurrences of the Desired Combination<br />### In the table, there is only one cell that contains the code "SP". Therefore, there is only one occurrence of the desired combination.<br /><br />## Step 4: Calculate the Probability<br />### The probability of randomly choosing a pizza with sausage and pepperoni is the number of favorable outcomes divided by the total number of possible outcomes. This can be calculated as follows:<br />\[<br />\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{16}<br />\]
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