Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. according to a national center for health statistics, the lifetime odds in favor of dying from heart disease are 1 to 5, so the probability of dying from heart disease is $\frac{1}{5}$. a. true; if the odds in favor of event e are a to b, then the probability is $p(e)=\frac{a}{b}$. b. false; if the odds in favor of event e are a to b, then the probability is $p(e)=\frac{a}{a + b}$. c. true; if the odds in favor of event e are a to b, then the probability is $p(e)=\frac{a}{a + b}$. d. false, if the odds in favor of event e are a to b, then the probability is $p(e)=\frac{a}{b}$

Explanation:

The formula for probability \(P(E)\) when odds in favor of an event \(E\) are \(a\) to \(b\) is \(P(E)=\frac{a}{a + b}\), not \(\frac{a}{b}\). Here \(a = 1\) (odds in favor) and \(b=5\) (odds against). The correct probability would be \(P(E)=\frac{1}{1 + 5}=\frac{1}{6}\), so the given statement is false.

Answer:

B. False, if the odds in favor of event \(E\) are \(a\) to \(b\), then the probability is \(P(E)=\frac{a}{a + b}\)