Suppose that A, B, and C are 3 independent events such that Pr(A)=1/4, Pr(B)=1/3 and Pr(C)=1/2.
a. Determine the probability that none of these events will occur.
Is it just:
(1-P(a))(1-P(b))(1-P(c)) = 3/4 * 2/3 * 1/2 = 1/4
The Attempt at a Solution
I tried to do 1. another way:
The probability that all theses events will occur: 1/4 * 1/3 * 1/2 = 1/24
1-(1/24) = 23/24
Obviously this is wrong. Is the reason it is wrong, because: the complement of "all of these events will occur" is that "not all of these events will occur," meaning, it is not "none of these events will occur."
None of these events will occur is included in the compliment 1-(1/24), but so is that 1 of the events occur, and that 2 of the events occur, etc.
Am I right in my reasoning?