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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
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Transcript text: 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
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Related content
Solution
Solution Steps
Step 1: Determine the Expected Number of Tails
When flipping a fair coin, the probability of landing tails up is p=21. If the coin is flipped N=450 times, the expected number of tails, E(T), can be calculated using the formula:
E(T)=N×p=450×21=225
Step 2: Interpret the Expected Value
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.
Step 3: Choose the Best Prediction
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
The best prediction is: D) Close to 225 times but probably not exactly 225 times