The probabilities of the independent events A and B are 0.4 and 0.5 respectively. Find the following probabilities:
a) The probability of A and B occurring.
b) The probability of A but not B occurring.
c) The probability of A or B occurring.
d) The probability of A or not B occurring.
e) The probability of A occurring given that B has occurred.
f) The probability of A occurring given that B has not occurred.