confusion in formula

probability that A and B will die in a year are p and q respectively.then the probability that only one of them will be alive at the end of the year
my solution
shall i use this formula here : p(AuB)=p(A)+p(B)-p(AnB)?

bhuvaneshnick said:

probability that A and B will die in a year are p and q respectively.then the probability that only one of them will be alive at the end of the year
my solution
shall i use this formula here : p(AuB)=p(A)+p(B)-p(AnB)?

Click to expand...

No, you should not use that formula. The reason is that in mathematics A u B means just A or just B OR BOTH. You do not want both!. I think this formula will be better--P ( A and B' ) + P ( A' and B), where A' means not A and (of course) B' means not B.
If you draw a venn diagram for p(A)+p(B)-p(AnB) you'll see that you are including the intersection, that is P(A U B).

Jomo said:

No, you should not use that formula. The reason is that in mathematics A u B means just A or just B OR BOTH. You do not want both!. I think this formula will be better--P ( A and B' ) + P ( A' and B), where A' means not A and (of course) B' means not B.
If you draw a venn diagram for p(A)+p(B)-p(AnB) you'll see that you are including the intersection, that is P(A U B).

Click to expand...

Let us assume for while that above is mutually exclusive events.Then p(AuB)=p(A)+p(B).Then we get probability of either one is going to die,isn't it?

Jomo said:

No, you should not use that formula. The reason is that in mathematics A u B means just A or just B OR BOTH. You do not want both!. I think this formula will be better--P ( A and B' ) + P ( A' and B), where A' means not A and (of course) B' means not B.
If you draw a venn diagram for p(A)+p(B)-p(AnB) you'll see that you are including the intersection, that is P(A U B).

Click to expand...

Let us assume for while that above is mutually exclusive events.Then p(AuB)=p(A)+p(B).Then we get probability of only one is going to die,isn't it?

bhuvaneshnick said:

Let us assume for while that above is mutually exclusive events.Then p(AuB)=p(A)+p(B).Then we get probability of only one is going to die,isn't it?

Click to expand...

P(a and b)=0 means that a and be can't happen at the same time. Now a and b are mutually exclusive means that a and b can't happen at the same time. So yes you are correct when you say that if a and b are mutually exclusive then P(a u b) = p(a) + P(b)
You say Then p(AuB)=p(A)+p(B).Then we get probability of only one is going to die,isn't it?. Well I have this exactness about things! The way I read what you wrote is that one of them will die--like the first one will die. I feel that you should say that one or the other but not both will die or exactly one will die.