To answer the questions in this problem, the following steps are advised:
Step 1: Compute the probability of obtaining a Red, Yellow, Green, and Blue color on each spin for both Mary and Nyla, as follows:
The probabilty of an outcome is generally defined as:
Now:
- For Mary:
![\begin{gathered} P(\operatorname{Re}d)=(9)/(40)=0.225\text{ (or 22.5 percent)} \\ P(Yellow)=(12)/(40)=0.3\text{ (or 30 percent)} \\ P(Green)=(9)/(40)=0.225\text{ (or 22.5 percent)} \\ P(Blue)=(10)/(40)=0.25\text{ (or 25 percent)} \end{gathered}]()
- For Nyla:
![\begin{gathered} P(\operatorname{Re}d)=(11)/(40)=0.275\text{ (or 27.5 percent)} \\ P(Yellow)=(10)/(40)=0.25\text{ (or 25 percent)} \\ P(Green)=(11)/(40)=0.275\text{ (or 27.5 percent)} \\ P(Blue)=(8)/(40)=0.20\text{ (or 20 percent)} \end{gathered}]()
Thus:
a) The expected out come for 100 spins are that:
For Mary:
![\begin{gathered} E(\operatorname{Re}d)=P(\operatorname{Re}d)*100=0.225*100=22.5 \\ E(Yellow)=P(Yellow)*100=0.3*100=30 \\ E(Green)=P(Green)*100=0.225*100=22.5 \\ E(Blue)=P(Blue)*100=0.25*100=25 \end{gathered}]()
- 22.5 (say, 22) of the total outcomes will be a Red colour
- 30 of the total outcomes will be a Yellow colour
- 22.5 (say, 22) of the total outcomes will be a Green colour
- 25 of the total outcomes will be a Blue colour
For Nyla:
![\begin{gathered} E(\operatorname{Re}d)=P(\operatorname{Re}d)*100=0.275*100=27.5 \\ E(Yellow)=P(Yellow)*100=0.25*100=25 \\ E(Green)=P(Green)*100=0.275*100=27.5 \\ E(Blue)=P(Blue)*100=0.20*100=20 \end{gathered}]()
- 27.5 (say, 27) of the total outcomes will be a Red colour
- 25 of the total outcomes will be a Yellow colour
- 27.5 (say, 27) of the total outcomes will be a Green colour
- 20 of the total outcomes will be a Blue colour
b) Mary and Nyla should not expect the same results after 100 spins because the results they each obtained after just 40 spins are markedly different. Also, the process is entirely random and the results cannot be predicted from the onset. Lastly, from the answers obtained in (a) Mary and Nyla should not expect the same outcome.
c) Their results might be different from the expected results based on theoretical probability because the results that are predicted by theoretical probability are for a very large number of spins.
That is, theoretical probability typically estimates what the results will be for a very large number of spins, say 1,000 or so.
Since the number of spins can practically not be that much, the results Mary and Nyla will obtain might be different from the expected results based on theoretical probability.