Question

Suppose a bag contains 13 red tokens and 19 green tokens that are well mixed. If you were to reach into the bag and pull out a token, what is the probability that the token is red? What is the probability that the token is green? If you reach into the bag and pull out two tokens and the first one is green, what is the probability that the second one is also green?

Answer 1

Answer with Explanation: The bag has 13red tokens and 19 green tokens:

The red probability:

$\begin{gathered} P_r=\frac{13_r}{(13_r+19_g)}=\frac{13}{32}= \\ \\ P_r=\frac{13}{32}=40.625\% \end{gathered}$

The Green probability:

$\begin{gathered} P_g=\frac{G}{T}=\frac{19_g}{(13_r+19_g)}=\frac{19}{32} \\ \\ P_g=\frac{19}{32}=59.375\% \end{gathered}$

If two tokes are pulled out, the first is green then the probability of the second to be green is:

$\begin{gathered} P_g=\frac{G}{T}=\frac{(19_g-1)}{(13_r+19_g)-1}=\frac{18}{31} \\ \\ P_g=\frac{18}{31}=58.065\% \end{gathered}$