Given that the coin is fair, the probability of getting tails or heads on any given flip is $\frac{1}{2}$ or 50%. Therefore, we can calculate the expected number of tails and heads if Jack flips the coin 163 times.

Expected Number of Tails in 163 Flips:

The expected number of tails is calculated as follows:

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

$\text{Expected Tails} = 163 \times 0.5 = 81.5$

Rounding to the nearest whole number:

$\text{Expected Tails} \approx 82$

Expected Number of Heads in 163 Flips:

Similarly, the expected number of heads is calculated as:

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

$\text{Expected Heads} = 163 \times 0.5 = 81.5$

Rounding to the nearest whole number:

$\text{Expected Heads} \approx 82$

Final Answers:

• Expected number of tails in 163 flips: 82
• Expected number of heads in 163 flips: 82

Would you like more details or have any other questions?

Here are five related questions:

1. What is the probability of getting exactly 82 tails in 163 flips?
2. How would the expected results change if the coin were biased?
3. What is the expected difference between the number of heads and tails after 163 flips?
4. If Jack observes 100 tails after 163 flips, how should he update his belief about the fairness of the coin?
5. How would you calculate the variance and standard deviation for the number of tails in 163 flips?

Tip: The expected number of outcomes is simply the probability of that outcome multiplied by the number of trials. This concept applies to many different situations in probability theory.