Suppose the probability of an event is [tex]\frac{37}{44}[/tex].

1. What are the odds for the event happening?
[tex]\square[/tex] to [tex]\square[/tex]

2. What are the odds against the event happening?
[tex]\square[/tex] to [tex]\square[/tex]



Answer :

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].