Question

I thought I knew how to do this but I don't

Answer 1

`\begin{gathered} (a)(5)/(7) \\ (b)(7)/(5) \end{gathered}`

Step-by-step explanation

(a) To find the odds in favor of Alonzo winning a medium stuffed animal, we have to divide the probability that he will win a medium stuffed animal by the probability that he will not win a medium stuffed animal.

There are 5 medium balloons out of 12 balloons in total, so, the probability that he will win a medium stuffed animal is:

`P(win)=(5)/(12)`

And the probability that he will not win a medium stuffed animal is:

`P(not-win)=1-(5)/(12)=(7)/(12)`

Therefore, the odds in favor of Alonzo winning a medium stuffed animal is:

`\begin{gathered} ((5)/(12))/((7)/(12))=(5)/(12)\cdot(12)/(7) \\ \Rightarrow(5)/(7) \end{gathered}`

In other words, the odds are 5 to 7.

(b) To find the odds against Alonzo winning a medium stuffed animal, we have to find the inverse of the odds of him winning or divide the probability that he will not win a medium stuffed animal by the probability that he will win a medium stuffed animal:

`\begin{gathered} ((7)/(12))/((5)/(12))=(7)/(12)\cdot(12)/(5) \\ \Rightarrow(7)/(5) \end{gathered}`

In other words, the odds are 7 to 5.