Question

find p(y|b) from the information in the table. to the nearest tenth, what is the value of p(y|b)? 0.2 0.3 0.4 0.5

Explanation:

Step1: Recall conditional - probability formula

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

Step2: Identify values from the table

From the table, $n(Y\cap B) = 34$ (the number in the cell where row $B$ and column $Y$ intersect), and $n(B)=96$ (the total number in row $B$).

Step3: Calculate the probability

$P(Y|B)=\frac{34}{96}\approx0.354$. Rounding to the nearest tenth, we get $0.4$.

Answer:

0.4