Random Variables and Discrete Probability Distribution

Question

X       6        8       10      12   14
P(X=x)  0.15    0.3     0.35    0.1   0.1

What is the probability that fewer than 8 or more than 12 use the lab in a given day?

Am I correct to say that I must just add 0.15 of X = 6 and 0.1 of X = 14?

Answer 1

You are correct. Remember however that the summation is allowed only because the events you are considering are disjoint. Basic probability rules tell us that the probability of the union of disjoint events reduces to the sum of the probabilities of the events.

$$P((X<8) \cup (X>12)) = P(X<8) + P(X>12) - P((X<8) \cap (X>12))$$

with the last term in the sum being $0$ because the event has zero probability.