Question

find p(y|b) from the information in the table.
to the nearest tenth, what is the value of p(y|b)?
table with rows x, y, z, total and columns a, b, c, total. data:
x: a=8, b=6, c=23, total=37
y: a=80, b=34, c=56, total=170
z: a=40, b=45, c=32, total=117
total: a=128, b=85, c=111, total=324
options: 0.2, 0.3, 0.4, 0.5

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(Y|B) = \frac{n(Y \cap B)}{n(B)} \), 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: Find \( n(Y \cap B) \) and \( n(B) \)

From the table:

• \( n(Y \cap B) \) (the number of elements in both \( Y \) and \( B \)) is 34.
• \( n(B) \) (the total number of elements in \( B \)) is 85 (from the "Total" row for column \( B \)).

Step3: Calculate \( P(Y|B) \)

Substitute the values into the formula: \( P(Y|B) = \frac{34}{85} \).
Simplify \( \frac{34}{85} = 0.4 \).

Answer:

0.4