The probability that event $$ A $$ will occur is $$ P(A)=0.32 $$. What is the probability (in decimal form) that event $$ A $$ will not occur? $$ P(\bar{A})=\square $$ to What are the odds for event $$ A $$ ? What are the odds against event $$ A $$ ? Simplify your answers.

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1. Given the probability of event $$ A $$ is  
   $$
   P(A)=0.32,
   $$  
   the probability that event $$ A $$ will not occur (its complement) is  
   $$
   P(\bar{A})=1-P(A)=1-0.32=0.68.
   $$

2. The odds for event $$ A $$ are defined as the ratio of the probability that the event occurs to the probability that it does not occur. Therefore,  
   $$
   \text{Odds for } A=\frac{P(A)}{P(\bar{A})}=\frac{0.32}{0.68}.
   $$  
   Multiply numerator and denominator by 100 to remove decimals:  
   $$
   \frac{32}{68}.
   $$  
   Simplify the fraction by dividing both terms by 4:  
   $$
   \frac{32 \div 4}{68 \div 4}=\frac{8}{17}.
   $$  
   So the odds for event $$ A $$ are $$ 8:17 $$.

3. The odds against event $$ A $$ are simply the inverse of the odds for $$ A $$. This means  
   $$
   \text{Odds against } A=\frac{P(\bar{A})}{P(A)}=\frac{0.68}{0.32}.
   $$  
   Again, multiply numerator and denominator by 100:  
   $$
   \frac{68}{32}.
   $$  
   Simplify by dividing both terms by 4:  
   $$
   \frac{68 \div 4}{32 \div 4}=\frac{17}{8}.
   $$  
   Thus, the odds against event $$ A $$ are $$ 17:8 $$.

Final answers:  
- $$ P(\bar{A})=0.68 $$  
- Odds for event $$ A $$: $$ 8:17 $$  
- Odds against event $$ A $$: $$ 17:8 $$
- The probability that event $$ A $$ will not occur is $$ 0.68 $$. - The odds for event $$ A $$ are $$ 8:17 $$. - The odds against event $$ A $$ are $$ 17:8 $$.

The probability that event will occur is .
What is the probability (in decimal form) that event will not occur? to
What are the odds for event ?
What are the odds against event ?
Simplify your answers.

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The probability that event will occur is . What is the probability (in decimal form) that event will not occur? to What are the odds for event ? What are the odds against event ? Simplify your answers.