Question

A number x is selected at random in the interval [-1, 1]. Let the events A={x<0}, B={|x-0.5|<1}, and C=x>0.75. Find P[A intersection B], P[A intersection C], P[AUB],P[AUC] and P[AUBUC].

Answer 1

The probability of an interval [a, b] , where -1 ≤ a ≤ 1 is $\frac{1}{2}(b-a)$

$P(B) = P(-0.5, 1) = \frac{3}{4} \\ P(A \cap B) = P(-0.5, 0) = \frac{1}{4} \\ P(A \cap C) = P(\oslash ) = 0 \\ P(A \cup B) = P(-1, 1) = 1 \\ P(A \cup C) = P((-1,0) \cup (0.75, 1)) = \frac{5}{8} \\ P(A \cup B \cup C) = P(-1,1) = 1$