Whether we like it or not, our life is full of all sorts of accidents, both pleasant and not very pleasant. Therefore, it would not hurt each of us to know how to find the likelihood of an event. This will help to make the right decisions in any circumstances that are associated with uncertainty. For example, such knowledge will be very useful when choosing investment options, assessing the possibility of winning a stock or lottery, determining the reality of achieving personal goals, etc., etc.
Probability Theory Formula
In principle, studying this topic does not take too much time. In order to get the answer to the question: “How to find the likelihood of any phenomenon?”, You need to understand the key concepts and remember the basic principles on which the calculation is based. So, according to statistics, the investigated events are denoted by A1, A2, ..., An. Each of them has both favorable outcomes (m) and the total number of elementary outcomes. For example, we are interested in how to find the probability that there will be an even number of points on the top face of the cube. Then A is a dice roll, m is a loss of 2, 4 or 6 points (three favorable options), and n is all six possible options.
The calculation formula itself is as follows:
P (A) = m / n.
It is easy to calculate that in our example, the desired probability is 1/3. The closer the result to unity, the greater the chance that such an event will actually happen, and vice versa. Here is such a theory of probability.
Examples
With one outcome, everything is extremely easy. But how to find the probability if the events go one after another? Consider this example: one card is shown from a card deck (36 pcs.), Then it is hidden again in a deck, and after mixing, the next one is pulled out. How to find the likelihood that in at least one case a lady of spades was pulled out? There is the following rule: if a complex event is considered, which can be divided into several incompatible simple events, then you can first calculate the result for each of them, and then add them together. In our case, it will look like this: 1/36 + 1/36 = 1/18 . But what about when several independent events occur simultaneously? Then we multiply the results! For example, the likelihood that when flipping two coins at once, two tails will fall out will be: ½ * ½ = 0.25.
Now let's take an even more complex example. Suppose we hit a book lottery in which ten of the thirty tickets are winning. It is required to determine:
- The likelihood that both will be winning.
- At least one of them will bring a prize.
- Both will be losing.
So, consider the first case. It can be divided into two events: the first ticket will be happy, and the second will also be happy. Consider that the events are dependent, because after each pulling the total number of options decreases. We get:
10/30 * 9/29 = 0.1034.
In the second case, you will need to determine the probability of a losing ticket and take into account that it can be either the first in a row or the second: 10/30 * 20/29 + 20/29 * 10/30 = 0.4598.
Finally, the third case, when you can’t even get one book from the lottery played: 20/30 * 19/29 = 0.4368.