# calculation of probability

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Refers to measure the degree of likelihood of a certain outcome when performing a random experiment or one that we cannot predict the outcome.

The likelihood values between 0 and 1 (or expressed as a percentage, between 0% and 100%):
- The zero value corresponds to the impossible event: throw a dice and the probability for number 7 is zero.
- The value corresponds to one certain event: throw a dice and the probability of getting any number from 1 to 6 is equal to one (100%).

All other events will be likely between zero and one: it will be greater the more likely it is that the event occurs. How to measure the probability? Favorable cases are divided among the possible cases. P (A) = favorable cases / possible cases. Sticking with the dice case, we have the following examples:

1. Probability of rolling a dice to get number 2: the favorable case is just one (which comes up the number 2) while there are six possible cases (can come up any number of 1 to 6). Therefore: Probability = 1/6 = 0.166 (or what is the same, 16.6%).
2. Probability of rolling a dice to get an even number: here are three favorable cases (comes up 2, 4 or 6), while six cases are still possible. Therefore: Probability = 3/6 = 0.50 (or what is the same, 50%).
3. Probability of rolling a dice to get fewer than 5: in this case we have four cases favorable (to get 1, 2, 3 or 4), compared with six cases. Therefore: Probability = 4/6 = 0.666 (or what is the same, 66.6%).
Sometimes, the probability that a given event occurs depends on whether another event has occurred previously or not. This is sometimes the fact that there is a certain phenomenon that can do more or less likely another fact to occur next. Such probabilities are called conditional probabilities, and are denoted by P (A / B) to the conditional probability of event A assuming that the event B has already occurred. The multiplicative law of probability indicates that the probability that two events occur simultaneously A and B equals: Probability (A y B) = P (A / B). P (B). The above multiplication law is also used to determine conditional probability P (A / B) from the values P (A and B) and P (B): Probability (A / B) = P (A and B) / P (B) where: - P (A / B) is the probability of that event A has been conditioned to the event given B. - P (B and A) is the probability of simultaneous occurrence of A and B - P (B) is the prior probability of the event B

Examples:
1. Someone rolls a dice and we know that the probability of rolling a 2 is 1/6 (prior probability). If we incorporate new information (for example, someone tells us that the result has been an even number) then the probability changes: P (A and B) = 1/6 P (B) = 1/2 P (A / B) = (1 / 6) / (1/2) = 1/3 then the probability that the number 2 if we know that has come up an even number is 1/3 (greater than the prior probability of 1/6).
2. A medical study has concluded that the probability that a person suffers coronary problems (event B) is 0.10 (a priori probability). Furthermore, the probability that a person suffering from obesity problems (event A) is 0.25 and the probability that a person suffers both obesity and coronary problems (event intersection of A and B) is 0.05. Calculate the probability that a person suffers heart problems if that person is obese (conditional probability P (B / A)). P (BYA) = 0.05 P (A) = 0.25 P (B / A) = 0.05 / 0.25 = 0.20