Shun is going to flip a fair coin $450$ times. $\newline$ Complete the following statement with the best prediction. $\newline$ The coin will land tails up... $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $175$ times $\newline$ (B) Close to $175$ times but probably not exactly $175$ times $\newline$ (C) Exactly $225$ times $\newline$ (D) Close to $225$ times but probably not exactly $225$ times

Full solution

Q. Shun is going to flip a fair coin

450

times.

\newline

Complete the following statement with the best prediction.

\newline

The coin will land tails up...

\newline

Choose

1

answer:

\newline

(A) Exactly

175

times

\newline

(B) Close to

175

times but probably not exactly

175

times

\newline

225

times

\newline

(D) Close to

225

times but probably not exactly

225

times

Understand expected outcome: The first step is to understand the expected outcome of flipping a fair coin multiple times. Since the coin is fair, the probability of landing tails up is $0.5$ (or $50\%$ ) for each flip. Therefore, if Shun flips the coin $450$ times, we expect half of those flips to result in tails.
Calculate expected number: To calculate the expected number of tails, we multiply the total number of flips by the probability of getting tails on a single flip. $\newline$ Expected number of tails = Total number of flips $\times$ Probability of tails $\newline$ Expected number of tails = $450 \times 0.5$ $\newline$ Expected number of tails = $225$
Interpret the results: Now we need to interpret the results. While the expected number of tails is $225$ , it is highly unlikely that Shun will get exactly $225$ tails due to the variability inherent in random events. The actual number of tails is likely to be close to $225$ , but not exactly $225$ .
Best prediction for statement: Based on the above reasoning, the best prediction for the statement is: $\newline$ ＂The coin will land tails up close to $225$ times but probably not exactly $225$ times.＂ $\newline$ This corresponds to option (D).