How to solve a problem with probability
Video: Probability Explained! 2024, July
The theory of probability in mathematics refers to its section that studies the laws of random phenomena. The principle of solving problems with probability is to clarify the ratio of the number of favorable outcomes for this event to the total number of outcomes.
Instruction manual
one
Read the condition of the task carefully. Find the number of favorable outcomes and their total number. Suppose you need to solve the following problem: in a box are 10 bananas, 3 of them are immature. It is necessary to determine the likelihood that a randomly taken banana will be ripe. In this case, to solve the problem, it is necessary to apply the classical definition of probability theory. Calculate the probability using the formula: p = M / N, where:
- M is the number of favorable outcomes, - N is the total number of all outcomes.
2
Calculate a favorable number of outcomes. In this case, it is 7 bananas (10 - 3). The total number of all outcomes in this case is equal to the total number of bananas, that is 10. Calculate the probability by substituting the values in the formula: 7/10 = 0.7. Therefore, the probability that a randomly taken banana is ripe will be 0.7.
3
Using the probability addition theorem, solve the problem if, according to its conditions, the events in it are incompatible. For example, in a needlework box there are spools of thread of different colors: 3 of them with white threads, 1 with green, 2 with blue and 3 with black. It is necessary to determine the likelihood that the spool removed will be with colored threads (not white). To solve this problem by the probability addition theorem, use the formula: p = p1 + p2 + p3 ….
4
Determine how many total coils are in the box: 3 + 1 + 2 + 3 = 9 coils (this is the total number of all outcomes). Calculate the probability of removing the coil: with green threads - p1 = 1/9 = 0.11, with blue threads - p2 = 2/9 = 0.22, with black threads - p3 = 3/9 = 0.33. Add the resulting numbers: p = 0.11 + 0.22 + 0.33 = 0.66 - the probability that the spool removed will be with colored thread. So, using the definition of probability theory, you can solve simple problems on probability.
note
To solve more complex problems on probability, the probability multiplication theorem, the Laplace, Bayes, and Bernoulli formulas are used, depending on the compatibility of events and the number of outcomes under the conditions of these problems.