find $p(y|b)$ from the information in the table. to the nearest tenth, what is the value of $p(y|b)$?\n| | x…
find $p(y|b)$ from the information in the table. to the nearest tenth, what is the value of $p(y|b)$?\n| | x | y | z | total |\n| a | 8 | 80 | 40 | 128 |\n| b | 6 | 34 | 45 | 85 |\n| c | 23 | 56 | 32 | 111 |\n| total | 37 | 170 | 117 | 324 |\n0.2\n0.3\n0.4\n0.5
Answer
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, $P(Y|B)=\frac{n(Y\cap B)}{n(B)}$, where $n(Y\cap B)$ is the number of elements in the intersection of $Y$ 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 $n(B)=85$ (the total number in row $B$).
Step3: Calculate the probability
$P(Y|B)=\frac{n(Y\cap B)}{n(B)}=\frac{34}{85}=0.4$
Answer:
0.4