The owner of a sushi restaurant looked over some recent orders. He noted how many yellowtail and salmon rolls had been ordered.

Question

Not spicy Spicy
Yellowtail 2 2
Salmon 3 4
What is the probability that a randomly selected sushi roll contains yellowtail and is not spicy?
Simplify any fractions.

Answer 1

To find the probability that a randomly selected sushi roll is yellowtail and not spicy, we need to follow these steps:

1. Determine the total number of sushi rolls.

   From the table provided:

   • Yellowtail rolls (not spicy) = 2
   • Yellowtail rolls (spicy) = 2
   • Salmon rolls (not spicy) = 3
   • Salmon rolls (spicy) = 4

   Now, let's calculate the total:

   \[ \text{Total rolls} = (2 + 2) + (3 + 4) = 4 + 7 = 11 \]

2. Identify the number of rolls that contain yellowtail and are not spicy.

   From the table, the number of yellowtail rolls that are not spicy is \(2\).

3. Calculate the probability.

   The probability \(P\) that a randomly selected sushi roll is yellowtail and not spicy is given by the formula:

   \[ P(\text{yellowtail and not spicy}) = \frac{\text{Number of yellowtail and not spicy rolls}}{\text{Total number of rolls}} = \frac{2}{11} \]

Thus, the probability that a randomly selected sushi roll is yellowtail and not spicy is \( \frac{2}{11} \).