Step 1 :There are 300 rolls of the die, and each roll has a probability of \(\frac{1}{2}\) of being odd.
Step 2 :We can find the expected number of odd rolls by multiplying the total number of rolls by the probability of a roll being odd: \(300 \times \frac{1}{2}\).
Step 3 :Calculating the expected number of odd rolls: \(300 \times \frac{1}{2} = \boxed{150}\)