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Chapter 8: Problem 101

Suppose a friend says he can predict whether a coin flip will result in heads or tails. You test him, and he gets 10 right out of \(20 .\) Do you think he can predict the coin flip (or has a way of cheating)? Or could this just be something that occurs by chance? Explain without doing any calculations.

Short Answer

Expert verified
The friend鈥檚 success rate (50%) is the same as the predicted chance outcome for a fair coin flip (50%). This suggests that the friend's success could be due to chance and doesn't necessarily mean he can predict the outcome or is cheating.

Step by step solution

01

Understand the Probability of a Single Coin Flip

Firstly, assess the likelihood of a single coin flip. For a fair, unbiased coin, there are two equally likely outcomes: heads or tails. Therefore, the probability of each outcome is \(0.5 .\)
02

Analyze the Friend's Success Rate

The friend predicts correctly 10 times out of 20. This is a 50% success rate, or in terms of probability, the friend鈥檚 guess resulted in the correct outcome with a probability of \(0.5 .\)
03

Compare the Results

The success rate of the friend is exactly the same as the expected rate of guessing randomly the result of any coin flip. Given this, the result can be explained by chance, and it doesn't indicate that the friend can predict coin flips or is somehow cheating.

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