Two or more events are said to be independent if the probability of occurrence of one event remains unaffected irrespective of whether the other event has occurred or not. Informally speaking this means that the two events have nothing to do with each other in the sense that there is the occurrence or non-occurrence of one event does not cause any change in the occurrence of the other event. We now list out seven real-life examples of independent events.
Examples of Independent Events:
- Suppose that we toss two unbiased dice. Let A be the event that we get a 6 on the first die and B be the event that we get a 6 in the second die. Then the events A and B are independent. This is because even if we get a 6 on the first die, it does not affect the outcome for the second die. The results obtained on the two dice are independent of each other.
- Suppose that a coin is tossed 10 times. Let A be the event that we obtain heads on the first 9 trials and let B be the event that we obtain heads on the last tenth trial. Suppose we are given that A has occured. Does this affect the occurence of B or not? Intuitively, one may feel that if we have obtained heads 9 times already then the probability of obtaining another head might be low. But this is false beacuse the probability of obtaining heads on the last try is still 50% beacuse each trial of the coin toss is independent of the preceeding one.
- Suppose that a jar contains 3 black balls and 3 white balls. Then the event of choosing a white ball first, REPLACING IT and then choosing a black ball are independent events. Note that if we do not replace the ball after choosing then the events will no longer be independent.
- Obtaining heads on a coin toss and obtaining an even number on a dice.
- Let A be the event the a person likes to drink coffee and let B be the event that the person likes to wear yellow shirts. Then the two events A and B are independent.