Jack flips a fair coin 50 times and sees heads 28 times. How many heads should he expect to see if he flips the coin 250 times? How many tails should he expect to see if he flips the coin 250 times? Round to nearest whole number as needed

To solve this problem, we start by understanding that a fair coin has an equal probability of landing heads or tails, which is \( \frac{1}{2} \) or 50%.

### Expected Number of Heads in 250 Flips:
Since each flip of the coin has a 50% chance of landing heads, the expected number of heads when flipping the coin 250 times can be calculated using the following formula:

\[
\text{Expected Heads} = \text{Total Flips} \times \text{Probability of Heads} 
\]

\[
\text{Expected Heads} = 250 \times 0.5 = 125
\]

### Expected Number of Tails in 250 Flips:
Similarly, since the probability of tails is also 50%, the expected number of tails in 250 flips can be calculated as:

\[
\text{Expected Tails} = \text{Total Flips} \times \text{Probability of Tails} 
\]

\[
\text{Expected Tails} = 250 \times 0.5 = 125
\]

### Final Answers:
- **Expected number of heads in 250 flips**: 125
- **Expected number of tails in 250 flips**: 125

Would you like more details or have any other questions?

Here are five related questions:
1. What is the probability of getting exactly 125 heads in 250 flips?
2. How does the number of trials affect the accuracy of the expected number of heads?
3. What is the probability of getting more than 150 heads in 250 flips?
4. If Jack saw heads 60% of the time after 50 flips, what does this imply about the fairness of the coin?
5. How does the Law of Large Numbers apply to this situation?

**Tip:** In probability, as the number of trials increases, the observed outcomes tend to approach the expected probabilities more closely due to the Law of Large Numbers.

Understand how to predict the expected number of heads and tails when flipping a fair coin, based on Jack's observations. Learn the application of probability concepts and the Law of Large Numbers in determining outcomes. Suitable for Grades 9-12.

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