Probability is one that measures the possibility of any event occurring in a mathematical problem and belongs to this branch of science that is responsible for studying events with the possible results that arise. In this article we show you some examples of it.
It depends more than anything on chance and each action is defined in the possibility that an event is feasible at the moment of giving a result among a specific number of times that represents the probability that that circumstance can occur.
Understand probability
A possible event is the eventuality that some phenomenon occurs a certain number of times, an example of which is rolling a 5 in a game of dice, the common response already stipulated being the fact that this object only has a number 5 on it. all their faces.
That is why the study of probability is given in the combination of several numbers so that the proposed events occur, hence the basis of statistics and belongs to the branch of mathematics that studies the eventuality that an event stimulates a result.
What do you need:
- First, the sample space of the probability, which is the number of possible results.
- In an essay or random sample, this concept is represented by the letter E.
- The event that is what you want to find out through the sample space.
- An example of an event might be getting heads or tails on a coin and the probability that either of them comes up in a given number of tosses.
- The quotient is the result that is generated or that has the same possibility of coming out of any experiment.
- This quotient is represented by the division of the number of suitable events between the possible cases.
- From the above, Laplace’s Law is recognized or called, an important element to realize the probabilities.
- Probability exercises generally have a small difficulty that can be solved slowly, but with perseverance the answer is achieved.
- Look for possible exercises that are similar to the one presented and take it from the most complex or difficult to the easiest to understand the problem and give it a solution.
Instructions
For example, there are 10 balls of different colors in a box, of which 3 are red, and the contingency to find out is the probability that one of them will come out as the first event, this being our event to consult.
Probability is in charge of finding out or calculating if it is possible for a red ball to be drawn at first and the number of times it can occur, as well as speaking if it is very common for this event to be repeated several times.
For this reason, it is said that probability is an event linked to statistics, giving answers to the fact that a phenomenon occurs as many times as possible, measuring or determining the validity of the result that one wants to find out without leaving any doubt about it.
For this reason, probability measures the number of times a result is obtained to carry out a random experiment knowing in the end all the possible responses that a single event can generate under different specific conditions of the selection process.
Instructions on sample exercises
- Removing a ball with numbers from 10 to 20 from a box. Several questions are generated from this event, the first of which is the following if an easy-to-answer exercise is required: What is the probability of drawing a prime number? The number of favorable events and the number of possible events are calculated to find out the probability that this event occurs. It is assumed that there are 4 prime numbers from 11 to 20 as possible results, so this digit is taken to perform the operation. You already have the favorable events, now it’s your turn to find out what the possible events are, selecting the number 10, since it is the number of balls you have in the box. Generating a result at the end of the division between 4 and 10. So 4/10 is supposed to be the answer, but the most indivisible part is reached, resulting in 2/5.
- In a glass box there are 8 red spheres, 5 blue spheres and 7 black spheres. When drawing any ball, you want to calculate the following: The probability that a ball is red
P (Red) = 8/20 = 0.4
The probability that the ball is blue
P (Blue) = 5/20 = 0.2 The probability of drawing 7 black
P (Black) = 7/20 = 0.35 - A student wants to randomly answer two questions on a true and false test. What would be the sample space for this problem? The sample space is assumed to be the entire set of possible events or outcomes of the two answers you want to give, so it must be direct without decomposing. Therefore, the probability that you answer false to both questions would have the following result:
E = (F,F) (F,V) (V,F) (F,F) - Several friends are playing with a dice and by throwing it a tireless number of 1000 times, the following result usually comes out: E (1) = 117; E(2) = 545; E(3) = 30; f(4) = 105; E(5) = 100; E (6) = 103. With this information: a) Calculate the probability of each one and b) estimate the sum of the even numbers of the dice. (2, 4 and 6)
Solution:
E (1) = 117/1000 = 0.117 E (4) = 105/1000 = 0.105
E (2) = 545/1000 = 0.545 E (5) = 100 /1000 = 0, 1
E(3) = 30/1000 = 0.03 E(6) = 103/1000 = 0.10 P(2), P(4) and P(6) = 0.545 + 0.105 + 0.103 = 0.753 - Calculate the probability of getting five FIVES when rolling five dice at the same time:
Solution: P (5,5,5,5,5,) = 1/5. 1/5. 1/5. 1/5. 1/5 = (1/5)5 = 1/3125
Tips
- View problems as easy to solve and approach them by trying to understand the steps from the beginning.
- Do them actively and in a group to see who can come up with the correct answer and thus understand them better.
- Rejoice when you have found the correct answer immediately or even after a long time.
- Carry out competitions about who can give a feasible answer to the questions that are asked about probability.
- Enter probability problems with a positive attitude, as well as the positivity of finding the correct answer quickly and effectively.
- Be confident enough that you can come up with the right answer from the start.
- Be patient and constant to solve probability problems, everyone has their logical moment.
- The greatest concentration must prevail since if you get distracted you will not understand a problem and find the solution to it immediately.
- Understanding a problem can take time, but with serenity you can achieve it.
- Read the statements of the problems well, many times the answer is hidden in them.
- Know in advance that you should consult with a problem similar to the one you are trying to solve and generate possible answers from it.
- Always positive attitude when solving problems, in addition to spending time to do them efficiently and correctly.
- Understand the nature of the problem, extract the data that is offered to you and enter the ones that are requested, in addition to devising a way to solve it quickly.
- Re-evaluate the exercise and review the answers and results that can be obtained to find out if the answer has been given correctly.