Hi sud21!sud21 wrote:
I would be very leery of questions posted from unknown sources. Unfortunately, there is no way to answer this question in the form given. We might think this is as simple as multiplying the Pr(NOT A) times Pr(NOT B) = 1/5, but this will not always be the case. We need to know more about the events in terms of their dependence. Here are 2 examples of what I mean.
For the following 2 examples, let's pretend that we have a 10 sided die with the numbers 1-10 on the sides (to keep the probabilities the same.
Example 1
Event A = rolling an even number (2, 4, 6, 8, 10 are successes) = 0.5 probability
Event B = rolling a number >=5 (5, 6, 7, 8, 9, 10 are successes) = 0.6 probability
Now, if we use simple formulas:
Pr(A&B) = (0.5)(0.6) = 0.3
Pr(A only) = Pr(A & NOT B) = (0.5)(1-0.6) = (0.5)(0.4) = 0.2
Pr(B only) = Pr(B & NOT A) = (0.6)(1-0.5) = (0.6)(0.5) = 0.3
Pr(Neither) = Pr(NOT A & NOT B) = (1-0.5)(1-0.6) = (0.5)(0.4) = 0.2
Let's check this by looking at the actual outcomes for each probability:
Pr(A&B) = (6, 8, 10) = 3/10 = 0.3
Pr(A only) = (2, 4) = 2/10 = 0.2
Pr(B only) = (5, 7, 9) = 3/10 = 0.3
Pr(Neither) = (1, 3) = 2/10 = 0.2
These all check out, so it would seem as if the basic formulas work...BUT, what if we change the definition of event A...
Example 2
Event A = rolling a number >=6 = (6, 7, 8, 9, 10) = 0.5 probability
Event B = rolling a number >=5 = (5, 6, 7, 8, 9, 10) = 0.6 probability
The probabilities we calculated above would still be the same mathematically...but when we actually look at the results, we see that they SHOULD be different:
Pr(A&B) = (6, 7, 8, 9, 10) = 5/10 = 0.5
Pr(A only) = (empty) = 0.0
Pr(B only) = (5) = 1/10 = 0.1
Pr(Neither) = (1, 2, 3, 4) = 4/10 = 0.4
So you can see, there is no way to answer this question unless we know that the events are "independent"!
Whit
