[tex]\text{odds}=\text{ 2:}7[/tex]
Explanation
Step 1
find the probability:
Probabllity is the chance that a particular event will occur expressed on a linear scale from 0 to 1
The formula to calculate the probability of an event is as follows
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]
a) Let
[tex]\begin{gathered} \text{favorable outcome= a blue marble = 2 ( there are 2 blue marbles)} \\ \text{total outcomes = 9 ( there are 9 marbles)} \end{gathered}[/tex]
now, replace
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P=\frac{2}{9} \end{gathered}[/tex]
Step 2
find the odds
The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.
[tex]\text{odsds}=\frac{P}{1-P}=\frac{\frac{2}{9}}{1-\frac{2}{9}}=\frac{\frac{2}{9}}{\frac{7}{9}}=\frac{2\cdot9}{7\cdot9}=\frac{2}{7}[/tex]
odds: 2:7
I hope this helps you
