P(y < 0.5 or y > 0.8) =  P(y < 0.5) + P(y > 0.8) = 1 − P(0.5 < y < 0.8) = 0.7
The probability of a single event is zero:
P(y = 1) = (1 − 1)*1 = 0
Intervals
pThe probability of a single event is meaningless for a continuous sample space. Only intervals can have a non-zero probability, represented by the area under the density curve for that interval.
Height
= 1
y
The probability of an interval is the same whether boundary values are included or excluded:
P(0 ≤ y ≤ 0.5) = (0.5 − 0)*1 = 0.5
P(0 < y < 0.5) = (0.5 − 0)*1 = 0.5
P(0 ≤ y < 0.5) = (0.5 − 0)*1 = 0.5