The phrase “if the selected dish contains” signals conditional probability: you already know something about the dish. In a two-way table, use the total for that known group as the denominator. Then find the cell where that group meets the category the question asks about. Restrict first, then count. Using the grand total ignores what you already know.
Hints
- Hint 1
The words “If the selected dish contains strain X” give a condition, a fact you already know about the dish. Which column contains every dish that could still have been selected?
- Hint 2
Find the A row inside the Strain X column. Their intersection is the cell shared by that row and column. Why would the total for the entire A row count too many dishes?
Step-by-step
Restrict to the Strain X column
Step 1Choose the group that is still possible
No Desmos needed. Read the counts directly from the table.
The phrase “If the selected dish contains strain X” is a condition: the dish is already known to be strain X. So only the Strain X column remains possible. Its total is , making the denominator, not all dishes.
- Step 2
Count the dishes from A in that group
The A row meets the Strain X column at . So dishes meet both requirements. The A row’s total, , includes strain Y dishes, so it cannot be the count of strain X dishes from A.
- Step 3
Write the probability
A conditional probability puts the count you want over the total in the known group:
The bar means “given that.” So the probability that a strain X dish came from refrigerator A is . Choice B.