Chapter 2 Probability - 2.4 Conditional Probability - Questions - Page 45: 37

$0.415=41.5$%

$P(3.5\lt GPA\lt4.0)=0.25$ $P(3.0\lt GPA\lt3.5)=0.35$ $P(GPA\lt3.0)=0.4$ $P(Getting~into~medical~school|3.5\lt GPA\lt4.0)=\frac{8}{10}=0.8$ $P(Getting~into~medical~school|3.0\lt GPA\lt3.5)=\frac{5}{10}=0.5$ $P(Getting~into~medical~school|GPA\lt3.0)=\frac{1}{10}=0.1$ $P(Getting~into~medical~school)=P(Getting~into~medical~school|3.5\lt GPA\lt4.0)P(3.5\lt GPA\lt4.0)+P(Getting~into~medical~school|3.0\lt GPA\lt3.5)P(3.0\lt GPA\lt3.5)+P(Getting~into~medical~school|GPA\lt3.0)P(GPA\lt3.0)=0.8\times0.25+0.5\times0.35+0.1\times0.4=0.415$