Question

events e and f are mutually exclusive, with p(f)=0.54 and p(e or f)=0.64. calculate the following and enter your answer one digit per box (please round your numbers to the extent possible). odds for e are: to odds against e are: to

Explanation:

Step1: Find \(P(E)\)

Since \(E\) and \(F\) are mutually - exclusive, \(P(E\cup F)=P(E)+P(F)\). Given \(P(F) = 0.54\) and \(P(E\cup F)=0.64\).
By the formula \(P(E)=P(E\cup F)-P(F)\), we have \(P(E)=0.64 - 0.54=0.1\).

Step2: Calculate the odds for \(E\)

The formula for odds for an event \(E\) is \(\text{Odds for }E=\frac{P(E)}{1 - P(E)}\).
Substitute \(P(E)=0.1\) into the formula: \(\frac{0.1}{1 - 0.1}=\frac{0.1}{0.9}=\frac{1}{9}\), so the odds for \(E\) are \(1\) to \(9\).

Step3: Calculate the odds against \(E\)

The formula for odds against an event \(E\) is \(\text{Odds against }E=\frac{1 - P(E)}{P(E)}\).
Substitute \(P(E)=0.1\) into the formula: \(\frac{1 - 0.1}{0.1}=\frac{0.9}{0.1}=\frac{9}{1}\), so the odds against \(E\) are \(9\) to \(1\).

Answer:

Odds for \(E\) are: \(1\) to \(9\)
Odds against \(E\) are: \(9\) to \(1\)