It is found that when a particular 4-sided die is rolled a 1 occurs 26.9% of the time, a 2 occurs 23.8% of the time, a 3 occurs 24.2% of the time, and a 4 occurs 25.1% of the time.
a) If the die is rolled fifteen times, what is the probability that an odd number occurs exactly ten times?
b) What is the expected value of a single roll of the die?