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

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

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Make predictions

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

(C) Exactly

225

times

\newline

(D) Close to

225

times but probably not exactly

225

times

Understand the problem: Understand the problem. $\newline$ We need to predict how many times a fair coin will land tails up after $450$ flips. A fair coin has an equal chance of landing heads or tails, which is a $50\%$ chance for each side.
Calculate expected number: Calculate the expected number of tails. $\newline$ Since the probability of getting tails on any given flip is $\frac{1}{2}$ , we can predict the expected number of tails by multiplying the total number of flips by the probability of getting tails. $\newline$ Expected number of tails = Total number of flips $\times$ Probability of tails $\newline$ Expected number of tails = $450 \times \frac{1}{2}$
Perform calculation: Perform the calculation for the expected number of tails. $\newline$ Expected number of tails = $450 \times \frac{1}{2} = 225$
Interpret the result: Interpret the result. $\newline$ The calculation shows that the expected number of times the coin will land tails up is $225$ . However, this is a theoretical average, and in practice, the actual number might be close to $225$ but not exactly $225$ due to the randomness of each coin flip.
Choose best prediction: Choose the best answer based on the interpretation. $\newline$ The best prediction is that the coin will land tails up close to $225$ times but probably not exactly $225$ times.

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