Question

find p(c|y) from the information in the table. to the nearest tenth, what is the value of p(c|y)?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(C|Y)=\frac{P(C\cap Y)}{P(Y)}\). In terms of frequency from the table, \(P(C|Y)=\frac{n(C\cap Y)}{n(Y)}\), where \(n(C\cap Y)\) is the number of elements in both \(C\) and \(Y\), and \(n(Y)\) is the number of elements in \(Y\).

Step2: Identify the values from the table

From the table, \(n(C\cap Y) = 15\) (the cell where row \(C\) and column \(Y\) intersect) and \(n(Y)=30\) (the total of column \(Y\)).

Step3: Calculate the probability

Substitute the values into the formula: \(P(C|Y)=\frac{15}{30}\).
Simplify the fraction: \(\frac{15}{30}=0.5\).

Answer:

0.5