# Chapter 4 - Probability - 4-5 Multiplication Rule: Complements and Conditional Probability - Beyond the Basics: 35

a)0.0741 b)0.8. c)Inverse not correct. Many patients will have to undergo unnecessary treatments.

#### Work Step by Step

a)We know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, hence P(Malignant|Positive)=\frac{8}{8+100}=0.0741. b)We know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, hence P(Positive|Malignant)=\frac{8}{8+2}=0.8. c) 75% is much more than 0.0741=7.41%, hence the inverse is not correct. Hence many patients will have to undergo unnecessary treatments.

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