Question

ellen has music practice three days a week. she practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. one week is selected at random.
we know that for a probability distribution function to be discrete, it must have two characteristics. one is that the sum of the probabilities is one. what is the other characteristic?
○ the probability of success is not the same from trial to trial.
○ the probability of failure is not the same from trial to trial.
○ each probability is between zero and one, inclusive.
○ each probability is between negative one and positive one, inclusive.
○ the product of the probabilities is one.

Explanation:

To determine the other characteristic of a discrete probability distribution function, we recall the properties: 1) The sum of all probabilities is 1. 2) Each individual probability must lie between 0 and 1 (inclusive), as probability can't be negative (eliminating the option about negative - positive one range) and the product of probabilities isn't a requirement (eliminating that option), and the first two options about success/failure probability per trial relate to binomial distributions (not a general discrete distribution property). So the correct characteristic is that each probability is between zero and one, inclusive.

Answer:

C. Each probability is between zero and one, inclusive.