# Thread: Probability-neither A nor B

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## Probability-neither A nor B

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

2. Good post? |
Is it .1?

3. Good post? |
Nopes,cloud

4. Good post? |
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)
=> 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

5. Good post? |
interesting,this the fisrt time I come across such a question!
Thanks guys!

6. Good post? |
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

7. Good post? |
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

8. Good post? |
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

9. Good post? |
Originally Posted by sdasar
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

10. Good post? |
Originally Posted by jjaacc
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