1Hmm... so it depends on whether they are mutually exclusive or not .. but not only on that factor right ?
If they are mutually exclusive, P(A∩B) = 0 .. but if they are not, it may/mayn't be 0.
Assertion:
If the probability of an event A is 0.4 and that of B is 0.3,then the probability of neither A nor B occuring depends upon the fact that A and B ,are mutually exclusive or not
Reason:
Two events are mutually exclusive if they dont occur simultaneously
a)Assertion and reason are correct and reason explains assertion
b)Assertion and reason are correct,but reason doesn't explain
assertion
c)Assertion is wrong,reason is correct
d)assertion is correct,reason is wrong
** This qeustion was given by one of our users... i din like it.. I believe that this is not a well framed question...
I wud like to see some of ur comments on the same :)
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9 Answers
1I think both the statements are correct and it is (a)... I don't understand why this isn't a well framed question ....
62Even i said to Krishna that i wud go for "A"
Btw this was a narayana question. and even the sir said. it could be both. (Not that we should give too much weight to his opinion!)
Why i said that this is not a well framed question is bcos the reason is not explained well enuf.
i mean that u need to have a margin where u say that this reason explains the assertion enuf...
See the correct reason for the above in my eyes is Independence of A and B! Or even if someone said Venn Diagram kind of stuff!
1If the probability of an event A is 0.4 and that of B is 0.3,then the probability of neither A nor B occuring depends upon the fact that A and B ,are mutually exclusive or not
If they are mutually exclusive, then the prob of them not occurring simultaneously will be 1-P(A)-P(B)..
If they can occur simultaneously, then 1-P(A)-P(B)+P(A∩B) ..
So, I concluded that it was correct reason ..
Edit: I meant, if they are not simultaneous, P(A∩B) = 0. So it depends on P(A∩B) = 0 which depends on whether they are mutually exclusive or not ..
62suppose that P(A∩B)=0 for a non exclusive case
Like universal set is [0,1] on the real line
A=[0,0.4]
B=[0.4,0.7]
Then A and B are not exclusive.. but still
P(A∩B) = 0
62That is the point varun..
P(A∩B) = 0 does not imply
that (A∩B) is empty set.. my example above!
162yes varun...
But suddenly i have started to think that the assertion itself is wrong.. what say? :D
1Lol that was what I first thought after seeing your example !!
I think it will be more apt if we say that it depends on whether P(A∩B) = 0 or not... :D
62So i think we can converge on the thing that
(C) is the correct answer because the assertion itself is wrong!!