Conditional Probability

Learn conditional probability, reversing a condition.

Lesson 2 of 32 parts Practice Flashcards

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Conditional Probability

Objective: Explain conditional probability, apply the stated method, and check its conditions.

For P(B)>0, P(A|B)=P(A∩B)/P(B). Conditioning restricts the reference set to B. In a table, divide the matching cell by the B margin, not the grand total. The conditional probability can differ from the unconditional P(A). The condition determines the denominator.

Formulas

$P(A|B)=P(A∩B)/P(B)$

Worked examples

Try itAmong 91 synthetic students who take science, 42 also take art. Find P(art | science).Show answer

Step 1: Conditioning restricts the denominator to science students. Step 2: Use 42/91. Step 3: The conditional probability is 6/13.

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Conditional Probability

Objective: Explain conditional probability, apply the stated method, and check its conditions.

Formulas

$P(A|B)=P(A∩B)/P(B)$

Worked examples

Try itAmong 91 synthetic students who take science, 42 also take art. Find P(art | science).Show answer

Step 1: Conditioning restricts the denominator to science students. Step 2: Use 42/91. Step 3: The conditional probability is 6/13.

Reversing a Condition

Objective: Explain reversing a condition, apply the stated method, and check its conditions.

P(A|B) and P(B|A) share a joint numerator but use different denominators. They are not generally equal. Name the condition before reading a two-way table; the reference group is the event after the conditioning bar. Reversing the condition generally changes the probability.

Formulas

$P(A|B)=joint/P(B); P(B|A)=joint/P(A)$

Worked examples

Try itIn a synthetic study, 42 students take both art and science, and 91 take art. Find P(science | art).Show answer

Step 1: The given condition is art, so use the art total. Step 2: Divide the both-subject count by 91. Step 3: The answer is 6/13; reversing a condition changes the denominator.

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