Da_Gr8_Mperor Posted May 13, 2006 Share Posted May 13, 2006 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? 0.5 0.6 0.1 0.9 0.2 Quote Link to comment Share on other sites More sharing options...
Cloudnineast Posted May 13, 2006 Share Posted May 13, 2006 Is it .1? Quote Link to comment Share on other sites More sharing options...
Da_Gr8_Mperor Posted May 13, 2006 Author Share Posted May 13, 2006 Nopes,cloud Quote Link to comment Share on other sites More sharing options...
GMAT-HELP Posted May 13, 2006 Share Posted May 13, 2006 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 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) => 0.9 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 Quote Link to comment Share on other sites More sharing options...
Trouble Posted May 13, 2006 Share Posted May 13, 2006 interesting,this the fisrt time I come across such a question! Thanks guys! Quote Link to comment Share on other sites More sharing options...
sdasar Posted May 13, 2006 Share Posted May 13, 2006 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 Quote Link to comment Share on other sites More sharing options...
GMAT-HELP Posted May 13, 2006 Share Posted May 13, 2006 Sdasar, I got the same ans as you did but I was wondering what happens in the scenario where B is a subset of A, then P(A or B) would be 0.5? and neither A nor B would be 0.5 too? Thanks, GMAT-HELP Quote Link to comment Share on other sites More sharing options...
sdasar Posted May 14, 2006 Share Posted May 14, 2006 GMAT-HELP, 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. Thanks, sdasar Quote Link to comment Share on other sites More sharing options...
jjaacc Posted May 14, 2006 Share Posted May 14, 2006 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 Sdasar: how do you get P(both events won't happen) = 0.3? Gmathelp: like your 2nd explanation. thanks Quote Link to comment Share on other sites More sharing options...
GMAT-HELP Posted May 14, 2006 Share Posted May 14, 2006 Sdasar: how do you get P(both events won't happen) = 0.3? Gmathelp: like your 2nd explanation. thanks P(both events won't happen) = p(A won't happen)*p(B won't happen) = 0.6*0.5 = 0.3 Quote Link to comment Share on other sites More sharing options...
jjaacc Posted May 14, 2006 Share Posted May 14, 2006 Understood. Cheers. Quote Link to comment Share on other sites More sharing options...
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