P(1≤x≤3) defined the probability that the result is between 1 and 3, included. You can answer this question in two ways:
1. Sum the probabilities of good events:
From the graph, we have
[tex] P(x=1) = 0.32,\quad P(x=2) = 0.24,\quad P(x=3) = 0.28 [/tex]
So,
[tex] P(1\leq x \leq 3) = 0.32+0.24+0.28 = 0.84 [/tex]
2. Use complementary probabilities
Asking that the result is 1, 2 or 3 is the same as asking that the result is not 4. The probability that the result is 4 is 0.16, so the probability that the result is not 4 will be
[tex] P(x\neq 4) = 1-P(x=4) = 1-0.16=0.84 [/tex]
The result is obviously the same.
