Question

find \\(p(y|b)\\) from the information in the table.

\\(\

$$\begin{array}{|c|c|c|c|c|}\\hline & x & y & z & \\text{total} \\\\\\hline a & 8 & 80 & 40 & 128 \\\\\\hline b & 6 & 34 & 45 & 85 \\\\\\hline c & 23 & 56 & 32 & 111 \\\\\\hline \\text{total} & 37 & 170 & 117 & 324 \\\\\\hline\\end{array}$$

\\)

to the nearest tenth, what is the value of \\(p(y|b)\\)?

\\(\bigcirc\\) 0.2
\\(\bigcirc\\) 0.3
\\(\bigcirc\\) 0.4
\\(\bigcirc\\) 0.5

Explanation:

Identify the formula for conditional probability

Using the Conditional Probability Calculation and Two-Way Frequency Tables knowledge points

$$ P(Y|B) = \frac{P(Y \cap B)}{P(B)} = \frac{\text{Frequency of } (Y \cap B)}{\text{Total frequency of } B} $$

Extract values from the table

Using the Two-Way Frequency Tables knowledge point

$$
LATEXBLOCK0
$$

Calculate the conditional probability

Using the Conditional Probability Calculation knowledge point

$$ P(Y|B) = \frac{34}{85} = 0.4 $$

Answer:

• 0.2
• 0.3
• 0.4 (Correct answer)
• 0.5