Ramkin is going to flip a fair coin $1200$ times. $\newline$ What is the best prediction for the number of times that the coin will land heads up? $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $50$ times $\newline$ (B) Close to $50$ times but probably not exactly $50$ times $\newline$ (C) Exactly $600$ times $\newline$ (D) Close to $600$ times but probably not exactly $600$ times

Full solution

Q. Ramkin is going to flip a fair coin

1200

times.

\newline

What is the best prediction for the number of times that the coin will land heads up?

\newline

Choose

1

answer:

\newline

(A) Exactly

50

times

\newline

(B) Close to

50

times but probably not exactly

50

times

\newline

600

times

\newline

(D) Close to

600

times but probably not exactly

600

times

Question Prompt: The question prompt is: ＂What is the best prediction for the number of times that the coin will land heads up after flipping a fair coin $1200$ times?＂
Coin Probability: A fair coin has two sides, heads and tails, and each side has an equal probability of landing face up on any given flip. Therefore, the probability of getting heads on a single flip is $\frac{1}{2}$ .
Calculate Expected Value: To predict the number of times the coin will land heads up after $1200$ flips, we can use the expected value. The expected value is calculated by multiplying the probability of an event by the number of trials. In this case, the event is landing heads up, and the number of trials is $1200$ flips.
Expected Value Calculation: Calculate the expected value for the number of times the coin will land heads up: Expected value = Probability of heads $*$ Number of flips = ($1/ $2$ ) $*$ $1200$ = $600$ $.
Best Prediction: The best prediction for the number of times the coin will land heads up is the expected value, which is $600$ times. However, while $600$ is the expected value, it is unlikely to be exactly $600$ due to the variability inherent in random events. The actual number will probably be close to $600$ , but not exactly $600$ .