A) The given information is:
The probability that Lena wins a movie ticket is 8/17.
This probability is given by:
[tex]P(winning)=\frac{favorable\text{ number of outcomes}}{total\text{ number of outcomes}}[/tex]The odds is favor are given by:
[tex]\text{ Odds in favor}=\frac{favorable\text{ outcomes}}{unfavorable\text{ outcomes}}[/tex]We can find the unfavorable outcomes by subtracting the number of favorable outcomes from the total number of outcomes, so:
Unfavorable outcomes=17-8=9.
So, the odds in favor are:
[tex]Odds\text{ }in\text{ }favor=\frac{8}{9}[/tex]B) The given information is:
The odds against Keith's favorite team winning are: 9/4
The odds against are given by:
[tex]Odds\text{ }against=\frac{\text{ unfavorable outcomes}}{\text{ favorable outcomes}}[/tex]The total number of outcomes is: unfavorable+favorable = 9+4=13
So, the probability of his favorite team winning is:
[tex]\begin{gathered} P(winning)=\frac{favorable\text{ outcomes}}{total\text{ number of outcomes}} \\ P(winning)=\frac{4}{13} \end{gathered}[/tex]