Question

If your chances of losing the shell game if you randomly pick is 2 in 3 what are the chances that you would lose 3 games in a row Answer the following problems using either addition rule make sure to reduce your fraction show all your work

Answer 1

Given that the cahnces of losing the shell game if you picked randomly is 2 in 3.

Let's find the chances that you would lose 3 games in a row.

The chance that you would lose one game is:

$\frac{2}{3}$

Therefore, to find the change that you would lose 3 games in a row, we have:

$(\frac{2}{3})^n$

Where n = 3.

Thus, we have:

$\begin{gathered} (\frac{2}{3})^3 \\ \\ =\frac{2}{3}\ast\frac{2}{3}\ast\frac{2}{3} \\ \\ =\frac{2\ast2\ast2}{3\ast3\ast3} \\ \\ =\frac{8}{27} \end{gathered}$

Therefore, the chances that you would lose 3 games in a row is:

$\frac{8}{27}$

ANSWER:

$\frac{8}{27}$