Whether you're a student or a professional, IDNLearn.com has answers for everyone. Ask any question and receive timely, accurate responses from our dedicated community of experts.

Four students are determining the probability of flipping a coin and it landing heads up. Each flips a coin the number of times shown in the table below.

\begin{tabular}{|c|c|}
\hline Student & Number of Flips \\
\hline Ana & 50 \\
\hline Brady & 10 \\
\hline Collin & 80 \\
\hline Deshawn & 20 \\
\hline
\end{tabular}

Which student is most likely to find that the actual number of times his or her coin lands heads up most closely matches the predicted number of heads-up landings?

A. Ana
B. Brady
C. Collin
D. Deshawn


Sagot :

To determine which student is most likely to find that the actual number of times their coin lands heads up closely matches the predicted number, we can use the Law of Large Numbers. The key idea here is that the more trials or flips that are performed, the closer the observed results will tend to be to the theoretical probability (which is 50% or 0.5 for a fair coin).

Let's consider each student and their number of flips:

- Ana flips the coin 50 times.
- Brady flips the coin 10 times.
- Collin flips the coin 80 times.
- Deshawn flips the coin 20 times.

According to the Law of Large Numbers, the student with the highest number of flips is most likely to have results that best match the predicted probability of heads, because a larger sample size reduces the effects of variance.

From the provided data:

- Ana: 50 flips
- Brady: 10 flips
- Collin: 80 flips
- Deshawn: 20 flips

Collin has the highest number of flips at 80.

Therefore, Collin is most likely to find that the actual number of times his coin lands heads up most closely matches the predicted number of heads-up landings, due to the larger sample size.