The probability that event A will happen is 0.5 and the event B will happen is 0.4. What is the range of the probability that neither A nor B will happen?
Range = max prob - min prob.
P(A or B) >= P(A)
P(A or B) >= P(B)
Editing..am still debating how to approach this pblm
0.5 <= P(A or B) <= 0.9
Range of P(A or B) = 0.4
I guess, my initial approach was in line with sdasar's explanation below:
maximize P(A or B)
P(A or B) = P(A) + P(B) - P(A&B)
for max prob => P(A&B) = 0 ( A and B are mutually exclusive)
neither = 0.1
minimize p(A or B) = p(A) + p(B) - P(A&B)
p(A&B) = p(A)*P(B) for independent events
= 0.5*0.4 = 0.2
p(A or B) = 0.7
neither = 0.3
Range = 0.3-0.1 = 0.2
Last edited by GMAT-HELP; 05-13-2006 at 09:05 PM.
The other way of doing is
When A & b are mutually independent events:
The probability that A won't happen is 0.5
The probability that B won't happen is 0.6
Probability that both events (neither A nor B) happen is 0.3
When A & B are mutually dependent(exclusive) events:
The probbality that either A or either B happen is 0.9 and none of them happen is 0.1
The range is 0.2
0.3 and 0.1 refers to well defined populations. One probablity refers to truly independent random events and the other to truly mutually exclusive events.
If there is any bias between events A and B as you eluded, all bets are off. I don't think the problem (based on the answers) is implying anything other than the above scenarios.
There are currently 1 users browsing this thread. (0 members and 1 guests)