Question

a researcher randomly asked 284 people how they prefer their eggs cooked and if they prefer orange juice or coffee with their breakfast. the two - way table displays the data. suppose a survey respondent is randomly selected. let event f = fried eggs and let event o = orange juice. what is the value of p(o|f)?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of a two - way table, if \(A = O\) (orange juice) and \(B = F\) (fried eggs), then \(P(O|F)=\frac{\text{Number of people who like fried eggs and orange juice}}{\text{Number of people who like fried eggs}}\).

Step2: Identify the values from the table

From the table, the number of people who like fried eggs (\(F\)) is \(n(F)=91\), and the number of people who like fried eggs and orange juice (\(F\cap O\)) is \(n(F\cap O) = 41\).

Answer:

\(\frac{41}{91}\)