A number x is selected at random in the interval [−1, 2]. Numbers from the subinterval [0, 2] occur half as frequently as those from [−1, 0). Let the events A x = < { 0},
B x =− < { 0.5 0.5}, and C x = > { 0.75}.
a) Find the probability assignment for an interval completely within [−1, 0); completely
within [0, 2] ; and partly in each of the above intervals.
b) Find the probabilities of A B A B and A C ,, , ∩ ∩ .
c) Find the probabilities of A B A C and A B C ∪ ∪ ∪∪ ,, , first by directly evaluating the
sets and then their probabilities, and second, by using the appropriate axioms or
corollaries