question 21
if ( p(e)=0.22 ), 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
question 22
if ( p(e)=0.35 ), 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

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for odds
The formula for odds for an event $E$ is $\frac{P(E)}{1 - P(E)}$, and the formula for odds against an event $E$ is $\frac{1 - P(E)}{P(E)}$

## Step2: Calculate for $P(E)=0.22$
- Odds for $E$:
$$
\begin{align*}
\frac{P(E)}{1 - P(E)}&=\frac{0.22}{1 - 0.22}\
&=\frac{0.22}{0.78}\
&=\frac{22}{78}\
&=\frac{11}{39}
\end{align*}
$$
So the odds for $E$ are $11$ to $39$
- Odds against $E$:
$$
\begin{align*}
\frac{1 - P(E)}{P(E)}&=\frac{0.78}{0.22}\
&=\frac{78}{22}\
&=\frac{39}{11}
\end{align*}
$$
So the odds against $E$ are $39$ to $11$

## Step3: Calculate for $P(E)=0.35$
- Odds for $E$:
$$
\begin{align*}
\frac{P(E)}{1 - P(E)}&=\frac{0.35}{1 - 0.35}\
&=\frac{0.35}{0.65}\
&=\frac{35}{65}\
&=\frac{7}{13}
\end{align*}
$$
So the odds for $E$ are $7$ to $13$
- Odds against $E$:
$$
\begin{align*}
\frac{1 - P(E)}{P(E)}&=\frac{0.65}{0.35}\
&=\frac{65}{35}\
&=\frac{13}{7}
\end{align*}
$$
So the odds against $E$ are $13$ to $7$

# Answer:
Question 21:
a) $11$ to $39$
b) $39$ to $11$
Question 22:
a) $7$ to $13$
b) $13$ to $7$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for odds

Step2: Calculate for \(P(E)=0.22\)

Step3: Calculate for \(P(E)=0.35\)

Answer: