Independent events are the events that occur without being dependent on any event. For instance, flipping two coins can get any outcome. Either Head or Tail. Both the flips’ products will be independent of each other.
Hence, if event A’s Probability of occurrence is not affected by event B’s occurrence, then A and B are said to be independent events. Consider an example of rolling a die. If A is the event ‘the number appearing is odd’ and B be the event ‘the number appearing is a multiple of 3’,
One of the examples can be rolling two dice rolls simultaneously. The result of both dice rolls will be independent of each other. Since both events do not affect the occurrence of each other, they are considered separate events. For another example, let us consider the trading domain. In the financial markets trading, a trader can trade in a collection of stocks, commodities and cash. In such a case, the trades are independent since trading in one market is independent of trading in another.
Also, an important point to note is that a trader could trade in both stocks, say, Microsoft, and in a commodity, say oil, for diversification.
The outcome of one event the work of one event affects the work of the other.
Does not affect the outcome of the other.
If two events are dependent, then the probability of both If two events, say A & B are independent events occurring is P (A and B) = P(A)Xu(B|A)
then the probability of both occurring is P (A and B) = P(A)pp. (B)
Before applying probability formulas, one needs to identify an independent event.
Check if one event affects the outcome of the other event? If yes, go to step 4, or else go to Step 3
The event is independent. Use the formula of separate occasions and get the answer.
The event is dependent. Use the formula of dependent event and get the answer.
The total probability of independent events by multiplying the likelihood of these events. Let us see with the help of examples:
Example 2: Two coins flip simultaneously. What is the chance of getting heads on either of these coins?
Answer: First thing that you realise is that these are independent events. Once you do that, move on to find the probability of each event. Let us call the first coin toss E and the second coin toss F. Therefore, we can write: P (E) = 1/2, i.e. probability of getting ahead on the first coin toss = 1/2.
Similarly, the probability of getting ahead on the second coin’s toss = 1/2. In other words, we can write that P (F) = 1/2.
Now we have to calculate the probability of both these events happening together. Hence we use the Rule of the product. If P is the probability of some event and Q is another event, then the likelihood of both P and Q happening together is P×Q.
Hence the probability that either of the two coins will turn up ahead = 1/2 × 1/2 = 1/4
Example 3: A die twice, and a coin is to twice. What is the probability that the dice will turn a six each time and the cash will turn a tail every time?
Answer: Each time the die is a company, it is a self-governing event. The probability of a getting a six is = 1/6. So the likelihood of getting a 6 when the die twice = 1/6 × 1/6 = 1/36
Similarly, the probability of getting a tail in two flips that follow each other (are independent) = (1/2) × (1/2) = 1/4
Therefore, as the two events, i.e. casting the die and tossing the coin, are independent, both events’ = (1/36) × (1/4) = 1/144.
The Rule of products is only applicable to the events independent of each other. The product gives the total probability of such events. In other words, the likelihood of all such events occurring is what we get from the development of possibilities.
Independence in real-world data sets, it’s rare to get perfectly equal probabilities. To some degree, all actual events that don’t involve games of chance are dependent.
We often accept that events are independent and test that assumption on sample data. If the chances are suggestively different, then we conclude the events are not separate. We’ll learn more about this development in inferential data.
Probability is the number of ways it can happen. Dependent Events such as removing marbles from a bag are affected by previous events. Independent events are not affected by previous events. We can6 calculate the probability of two or more Independent events by multiplying. Not all coincidences are improbable.