To solve this, we need to determine the odds for and against the event happening given the probability.
Given:
[tex]\[ \text{The probability of the event,} \, P(\text{event}) = \frac{37}{44} \][/tex]
1. Calculate the odds for the event happening:
The "odds for" an event is given by:
[tex]\[ \text{odds for} = \frac{P(\text{event})}{1 - P(\text{event})} \][/tex]
Substituting the given probability,
[tex]\[ \text{odds for} = \frac{\frac{37}{44}}{1 - \frac{37}{44}} = \frac{\frac{37}{44}}{\frac{7}{44}} = \frac{37}{7} \][/tex]
So, the odds for the event happening are [tex]\( 37 \)[/tex] to [tex]\( 7 \)[/tex].
2. Calculate the odds against the event happening:
The "odds against" an event is given by:
[tex]\[ \text{odds against} = \frac{1 - P(\text{event})}{P(\text{event})} \][/tex]
Using the given probability,
[tex]\[ \text{odds against} = \frac{\frac{7}{44}}{\frac{37}{44}} = \frac{7}{37} \][/tex]
So, the odds against the event happening are [tex]\( 7 \)[/tex] to [tex]\( 37 \)[/tex].
Therefore, the results are:
- The odds for the event happening are [tex]\( 37 \)[/tex] to [tex]\( 7 \)[/tex].
- The odds against the event happening are [tex]\( 7 \)[/tex] to [tex]\( 37 \)[/tex].
