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Mutually exclusive:-
Two events or two outcomes (say, A and B)are said to be mutually exclusive, if at a time occurence of one prevents the occurence of the other
Now, if there is an event say x, which is said to have occured if any one of those mutually exclusive events occurs (at a time), then the
probability of event X will be,
P(X) = P(A or B) = P(A) + P(B) ...(1)
SimplesT example:
Event of getting head or tail while tossing a coin = x
Probability of getting head = P(A) = 1/2
Probability of getting tail = P(B) = 1/2
Now,
Probability of X = P(X) = P(A or B) = P(A) + P(B) = 1/2 + 1/2 = 1
Independent:-
Two events are said to be independent of each other if, occurence of one doesn't affect the probability of the other event.
P(X) = P(A and B) = P(A).P(B)
Two events or two outcomes (say, A and B)are said to be mutually exclusive, if at a time occurence of one prevents the occurence of the other
Now, if there is an event say x, which is said to have occured if any one of those mutually exclusive events occurs (at a time), then the
probability of event X will be,
P(X) = P(A or B) = P(A) + P(B) ...(1)
SimplesT example:
Event of getting head or tail while tossing a coin = x
Probability of getting head = P(A) = 1/2
Probability of getting tail = P(B) = 1/2
Now,
Probability of X = P(X) = P(A or B) = P(A) + P(B) = 1/2 + 1/2 = 1
Independent:-
Two events are said to be independent of each other if, occurence of one doesn't affect the probability of the other event.
P(X) = P(A and B) = P(A).P(B)
for mutually exclusive:-
P(A and B) = P(A).P(B) = (1/2).(1/2) = 1/4 ....(considering the coin is tossed twice)
for independent:- (considering the same example as of mutually exclusive)
P(A or B) = P(A) + P(B) = 1/2 + 1/2 = 1
As i can see now that applying AND/OR operations in finding probability doesn't depend on the kind of events as i have thought of them earlier (like OR is used when we have to deal with the mutually exclusive events and AND is used when we have to deal with the independent events). AND/OR operations simply depends on the kind of problem that we are facing or solving. Like, if there is an event that depends on two other sub-events (known as compound events) and this event will be said to have occurred if any one of the sub-events occurs, then in that case OR operation will be used as is done in the above example. And in other case if the same event is said to have occurred if and only if both of the sub-events occurs then in that case AND operation will be used. And the important thing here is which i guess i know now is that those sub-events can be mutually exclusive events or independent events both.
But Steve the definitions that i wrote above for both i.e. mutually exclusive and independent events i read them from the book and the internet. So, i don't know why and how they looked similar in meaning to me but when i see their definitions i get confused and find myself unable to figure out whether they are really similar or different. So, please tell me now what is that exactly...
P(A and B) = P(A).P(B) = (1/2).(1/2) = 1/4 ....(considering the coin is tossed twice)
for independent:- (considering the same example as of mutually exclusive)
P(A or B) = P(A) + P(B) = 1/2 + 1/2 = 1
As i can see now that applying AND/OR operations in finding probability doesn't depend on the kind of events as i have thought of them earlier (like OR is used when we have to deal with the mutually exclusive events and AND is used when we have to deal with the independent events). AND/OR operations simply depends on the kind of problem that we are facing or solving. Like, if there is an event that depends on two other sub-events (known as compound events) and this event will be said to have occurred if any one of the sub-events occurs, then in that case OR operation will be used as is done in the above example. And in other case if the same event is said to have occurred if and only if both of the sub-events occurs then in that case AND operation will be used. And the important thing here is which i guess i know now is that those sub-events can be mutually exclusive events or independent events both.
But Steve the definitions that i wrote above for both i.e. mutually exclusive and independent events i read them from the book and the internet. So, i don't know why and how they looked similar in meaning to me but when i see their definitions i get confused and find myself unable to figure out whether they are really similar or different. So, please tell me now what is that exactly...
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Steve i think i have got the answer finally. Mutually exclusive and independent events are two different terms used in the field of probability.
If i toss a coin then getting a head is an event in itself and getting a tail is an another event. Now, if the case is coin is to be tossed just once then i would say that these two events are mutually exclusive because if head comes, happening of the other event i.e. getting a tail automatically becomes impossible. So, in tossing a coin once we find two mutually exclusive events.
Now, if the same coin is tossed twice then the probability of getting head with the first toss does not and can not affect the occurrence of the probability of getting tail on the
second toss and so here getting a head and getting a tail are two independent events.
Please tell me now if am right about these two events or not.
If i toss a coin then getting a head is an event in itself and getting a tail is an another event. Now, if the case is coin is to be tossed just once then i would say that these two events are mutually exclusive because if head comes, happening of the other event i.e. getting a tail automatically becomes impossible. So, in tossing a coin once we find two mutually exclusive events.
Now, if the same coin is tossed twice then the probability of getting head with the first toss does not and can not affect the occurrence of the probability of getting tail on the
second toss and so here getting a head and getting a tail are two independent events.
Please tell me now if am right about these two events or not.
