The first digits of numbers in legitimate records often follow a distribution known as Benford's Law. Here is the distribution.
First digit: 1 2 3 4 5 6 7 8 9
Probability: 0.305 0.172 0.125 0.097 0.079 0.067 0.058 0.058 0.039
P(A) = P(first digit is 1) = 0.305
P(B) = P(first digit is 6 or greater) = 0.222
P(C) = P(first digit is odd) = 0.606
We will define event D to be {first digit is less than 4}. Using the union and intersection notation, find the following probabilities.
(a) P(D)
(b) P(B ∪ D)
(c) P(Dc)
(d) P(C ∩ D)
(e) P(B ∩ C)