Question

question 23
4 pts
suppose events e and f are independent, with p(f) = 0.4831 and p(e∩f) = 0.231888. calculate the following and enter your answer one digit per box (please simplify your numbers to the extent possible).
a) the odds for e are: to
b) the odds against e are: to

Explanation:

Step1: Use the formula for independent events

For independent events \(E\) and \(F\), \(P(E\cap F)=P(E)\times P(F)\). Given \(P(F) = 0.4831\) and \(P(E\cap F)=0.231888\), we can find \(P(E)\) by \(P(E)=\frac{P(E\cap F)}{P(F)}\).

$$P(E)=\frac{0.231888}{0.4831}=0.48$$

Step2: Calculate the odds for \(E\)

The odds for an event \(E\) is given by \(\frac{P(E)}{1 - P(E)}\). Substituting \(P(E)=0.48\), we get \(\frac{0.48}{1 - 0.48}=\frac{0.48}{0.52}=\frac{12}{13}\)

Step3: Calculate the odds against \(E\)

The odds against an event \(E\) is given by \(\frac{1 - P(E)}{P(E)}\). Substituting \(P(E)=0.48\), we get \(\frac{1 - 0.48}{0.48}=\frac{0.52}{0.48}=\frac{13}{12}\)

Answer:

a) The odds for \(E\) are \(12\) to \(13\)
b) The odds against \(E\) are \(13\) to \(12\)