Question

Part A. Select the equation that best represents f(n), the number of yellow counters that land on yellow (and are put back into the bag) at the end of the trial n, when n>1?Part B.Using the equation you selected in Part A, determine how many trials the students would need to run until exactly one counter lands yellow side up (and is put into the bag)? Use mathematics to justify your response.

Answer 1

The experiment is equivalent to tossing 128 coins at the same time. The probability of a coin landing on heads (yellow) is 1/2. Therefore, if all the coins are fair, after one try, one-half of the coins will land on tails (red). So, only 128/2=64 coins are tossed the second time, and 1/2 of them will land on tails.

After repeating the experiment n times, the expected number of counters that land on yellow at the end of the trial is

$f(n)=128(\frac{1}{2})^n$

Part B)

Set f(n)=1 and solve for n, as shown below,

$\begin{gathered} f(n)=1 \\ \Rightarrow128(\frac{1}{2})^n=1 \\ \Rightarrow\frac{1}{2^n}=\frac{1}{128} \\ \Rightarrow2^n=128 \\ \Rightarrow n\log 2=\log 128 \\ \Rightarrow n=\frac{\log 128}{\log 2}=7 \\ \Rightarrow n=7 \end{gathered}$

Thus, after 7 trials, exactly one counter will land on yellow.