Question

question 4
1 pts
if ( p(e)=0.36 ), then calculate and find that (enter one digit per box after simplifying your numbers to the extent possible):
a) the odds for ( e ) are: to
b) the odds against ( e ) are: to

Explanation:

Step1: Calculate \(P(\overline{E})\)

We know that \(P(\overline{E})=1 - P(E)\). Given \(P(E) = 0.36\), then \(P(\overline{E})=1 - 0.36=0.64\).

Step2: Find the odds for \(E\)

The formula for odds for an event \(E\) is \(\frac{P(E)}{P(\overline{E})}\). Substituting the values, \(\frac{0.36}{0.64}=\frac{36}{64}=\frac{9}{16}\). So the odds for \(E\) is \(9\) to \(16\).

Step3: Find the odds against \(E\)

The formula for odds against an event \(E\) is \(\frac{P(\overline{E})}{P(E)}\). Substituting the values, \(\frac{0.64}{0.36}=\frac{64}{36}=\frac{16}{9}\). So the odds against \(E\) is \(16\) to \(9\).

Answer:

a) \(9\) to \(16\)
b) \(16\) to \(9\)