A fair 6-sided die has three odd numbers: 1, 3, and 5. Since half of the faces are odd (3 out of 6), the probability of rolling an odd number is:

$P(\text{odd number}) = \frac{3}{6} = \frac{1}{2}$

Now, if the die is rolled 360 times, the expected number of times an odd number will appear is:

$\text{Expected number of odd rolls} = P(\text{odd number}) \times 360 = \frac{1}{2} \times 360 = 180$

Thus, a reasonable prediction for the number of times the die will land on an odd number is 180.

Answer: 180

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Here are 5 related questions to expand on this topic:

1. What is the probability of rolling a 1 or 2 on a 6-sided die?
2. If you roll the die 600 times, how many times would you expect to roll a number greater than 4?
3. What is the expected value of a roll of a fair 6-sided die?
4. If you roll two dice, what is the probability of getting two odd numbers?
5. What is the standard deviation of the number of odd rolls in 360 rolls?

Tip: When dealing with probability, multiplying the probability by the number of trials gives you the expected count for that event.