I was referring to my probability notes and came upon this note :
Mutually exclusive events are choosen when events are raken from same experiment and independency is used when events are taken from different expeiments.
So if I toss two coins then the result of first toss and second toss is independent.Does that mean the first toss and second toss are different experiments?This is getting confusing for me because I always thought those two tosses to be of same experiment as we know the outcomes of this experiment even though we are not perfectly sure about the final result .Why do we have to consider them as different experiments and what happens if we don't consider them to be same?
Saying that "independent events are taken from different experiments" is (to me) misleading. Independence is a situation where knowing the results of one experiment doesn't give you any information about another experiment. For example, tossing coins. Tossing a coin once and getting, say, heads, will not tell you anything about what you're likely to toss the second time.
By contrast, consider these two experiments: You have a photometer (a light intensity meter) and a rain gauge; you intend to use these devices to gather weather information. Are the readings of these two devices independent? No, definitely not. If the rain gauge measures a lot of rain, the photometer is likely to measure low light intensity. Do they represent "different experiments"? Yes.
Also, "mutual exclusive" just means that two events cannot happen at the same time. For example, "the coin is heads" and "the coin is tails" are mutually exclusive. Or "there are no clouds in the sky today" and "my house was struck by lightning today" are mutually exclusive.