Questions: You might need: Calculator 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 Show Calculator Related content

Solution Steps

When flipping a fair coin, the probability of landing tails up is \( p = \frac{1}{2} \). If the coin is flipped \( N = 450 \) times, the expected number of tails, \( E(T) \), can be calculated using the formula:

\[ E(T) = N \times p = 450 \times \frac{1}{2} = 225 \]

The expected value \( E(T) = 225 \) indicates that, on average, the coin will land tails up 225 times out of 450 flips. However, due to the nature of probability and random events, the actual number of tails in a specific sequence of 450 flips may vary around this expected value.

Given the options:

• (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

The expected value \( E(T) = 225 \) matches option (C) exactly. However, in practice, the number of tails is likely to be close to 225 but not necessarily exactly 225 due to the variability inherent in random processes.

Final Answer