Question

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

Answer 1

ANSWER

$\begin{gathered} (a)\frac{5}{7} \\ (b)\frac{7}{5} \end{gathered}$

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:

$P(win)=\frac{5}{12}$

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

$P(not-win)=1-\frac{5}{12}=\frac{7}{12}$

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

$\begin{gathered} \frac{\frac{5}{12}}{\frac{7}{12}}=\frac{5}{12}\cdot\frac{12}{7} \\ \Rightarrow\frac{5}{7} \end{gathered}$

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:

$\begin{gathered} \frac{\frac{7}{12}}{\frac{5}{12}}=\frac{7}{12}\cdot\frac{12}{5} \\ \Rightarrow\frac{7}{5} \end{gathered}$

In other words, the odds are 7 to 5.