Question

if ( p(e)=0.26 ), then what are the odds against ( e )?
the odds against ( e ) are ( square ) to ( square ).
(simplify your answers.)

Explanation:

Step1: Find the probability of the complement of event \(E\)

The probability of the complement of event \(E\), denoted as \(P(\overline{E})\), is given by \(P(\overline{E})=1 - P(E)\).
Since \(P(E) = 0.26\), then \(P(\overline{E})=1 - 0.26=0.74\).

Step2: Calculate the odds against \(E\)

The odds against an event \(E\) is the ratio of \(P(\overline{E})\) to \(P(E)\).
The ratio \(\frac{P(\overline{E})}{P(E)}=\frac{0.74}{0.26}\).
Multiply numerator and denominator by 100 to get \(\frac{74}{26}\).
Simplify the fraction \(\frac{74\div2}{26\div2}=\frac{37}{13}\).

Answer:

The odds against \(E\) are \(37\) to \(13\).