GOZUNTA
Try it now
All courses Geometry · S-CP.5 44 of 57
Explain conditional probability and independence in everyday language and situations.

Identify and interpret the parts of a conditional probability statement

Problem
Interpret \(P(\text{recovery}|\text{treatment})=0.80\) in an among-group sentence, keeping treatment as the conditioned population and avoiding a causal claim.
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Let your results add up.

Each saved attempt adds useful evidence about what you have practiced and what deserves another pass.

Create a free account
With paid access

Separate understanding from one lucky answer.

Multiple variants of a problem type let you apply the method again before deciding that the skill is secure.

Compare plans

Hint

Read the expression from the bar outward: first identify the event after the bar, then the event before it.

In P(X|Y), Y is the condition/reference group and X is the target event measured within that group.

Solution walkthrough

01

Read target and condition

\[\text{target}=\text{recovery};~\text{condition}=\text{treatment}\]

In P(recovery|treatment), the event left of the bar is measured within the group right of the bar.

02

Convert the probability

\[0.80=80\%\]

Multiplying the decimal by 100 expresses the conditional rate as a percent.

03

Build the among-group sentence

\[\text{among}~\text{people}~\text{who}~\text{received}~\text{treatment},~80\%~\text{recovered}\]

The sentence begins with the conditioned population and then states the measured outcome rate.

04

Check the claim boundary

\[\text{this}~\text{describes}~\text{the}~\text{treated}~\text{group};~\text{it}~\text{does}~\text{not}~\text{prove}~\text{treatment}~\text{caused}~\text{recovery}\]

Conditional probability is descriptive unless a valid causal design supplies more evidence.

+

Another way

  1. Read left-to-right after naming the group: within treatment, recovery occurs with probability 0.80.

!

Common mistake

Do not reverse the condition to among recovered people, and do not add a causal verb.

Solution walkthrough video