A fair coin has two sides, heads or tails.The coin is flipped 80 times.Which result is most likely to happen?A73 tailsB10 tailsC42 tailsD59 tails

1. Break Down the Problem

To determine which result is most likely, we analyze the probabilities associated with each outcome of flipping a fair coin 80 times. Specifically, we want to find out which number of tails among 73, 10, 42, and 59 is closest to the expected number of tails.

2. Relevant Concepts

For a fair coin, the probability of getting tails on any single flip is $p = \frac{1}{2}$. The expected number of tails in 80 flips can be calculated using the formula: $\text{Expected Tails} = n \times p = 80 \times \frac{1}{2} = 40$

3. Analysis and Detail

Now, we can assess how far each of the options is from the expected number of tails (40):

• A) 73 tails: Difference from expected = $|73 - 40| = 33$
• B) 10 tails: Difference from expected = $|10 - 40| = 30$
• C) 42 tails: Difference from expected = $|42 - 40| = 2$
• D) 59 tails: Difference from expected = $|59 - 40| = 19$

4. Verify and Summarize

Among the differences calculated, 42 tails has the smallest difference from the expected value of 40, making it the most likely outcome when flipping the coin 80 times.

Final Answer

The most likely outcome is C) 42 tails.