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All courses Math II · S-CP.8 70 of 73
Apply and interpret the general Multiplication Rule with conditional probability.

Find a joint probability from a marginal probability and a conditional probability

Problem
Use P(A and B)=P(A)P(B|A) to multiply 0.40 by 0.25.
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Hint

Use the multiplication rule \(P(A and B)=P(A)\cdot P(B|A)\).

A conditional probability like \(P(B|A)\) tells you the chance of \(B\) happening once \(A\) has already happened.

Solution walkthrough

01

Use the conditional multiplication rule

\[P(A~\text{and}~B)=P(A)P(B|A)\]

A joint probability equals the first event probability times the conditional probability of the second.

02

Substitute

\[(0.40)(0.25)\]

The marginal P(A) is 0.40 and P(B given A) is 0.25.

03

Multiply

\[0.40*0.25=0.10\]

One quarter of 0.40 is 0.10.

04

Check

\[0.10/0.40=0.25\]

Dividing the joint result by P(A) recovers the supplied conditional probability.

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Another way

  1. Use fractions (2/5)(1/4)=1/10.

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Common mistake

Do not add 0.40 and 0.25; a joint path multiplies.