Probability is the possibility that an event occur. If we repeat many times an experiment, when obtained expected result, it is divided between number of experiments to know the probability. If a result is sure that occur the probability will be 1 (100%). If a event is sure that does not occur the probability will be 0.
Examples
ProbabilityFrequency (objective): Probability that an event will occur, is the probability of times that the result will be observed if we repeat the experiment many times.
Results for E. histolytica
n (%)Positive
59 (29.5)
Negative
151 (70.5)
An experiment is a process planed to obtain data.
Probability to have amebiasis is 59/200= 0.295= 29.5% Probability of does not have amebiasis es 151/200= 0.705 = 70.5% or 1 - 0.0.295=0.705 = 70.5%
Probability rules
Mutually excluded events Two events are mutually excluded if the occurrence of an event avoid the occurrence of the other. For example If a baby is male, cannot be female. If a child had positivity for E. histolytica, can not had negativity. The probability of occurrence of two mutually excluded events, is the probability of occurrence of an event or another, and we can obtain the probability, add the individual probabilities of each event.Probability rules
Example 100 new born in a maternity hospital 55 were females and 45 males Probability to be female 55/100 = 0.55 Probability to be male 45/100=0.45 Probability to be anyone = 0.55 + 0.45 = 1.00Probability rules
Example 200 children with a test for E. histolytica 59 had positive result. 151 had negative result Probability of positivity for E. histolytica was 59/200= 0.295 Probability of negativity for E. histolytica was 151/200 = 0.705 Probability for positive or negative result was 0.295 + 0.705 = 1.00Probability rules
Independent events Two events are independents if the occurrence of a event does not affect the occurrence of the second event. Example If the first new born is male, does not affect that the next be female. Probability of two independent events is obtained multiplying individual probabilities of each event. This is the multiplicative law of probability.Probability rules
In a blood bank, they determine blood groups:Group
n
%
0
45
45
A
29
29
B
21
21
AB
5
5
Total
100
100
What is the probability of next two persons will be 0 group? Is it mutually excluded or independent?
Probability rules
If the next person has 0 group does not interfere with that the second next person has 0 group, because of this are independent events. Their individual probabilities, are multiplied: 0.45 x 0.45 = 0.2025 = 20.25%Probability rules
Example 100 new born in a maternity hospital 55 were females and 45 males Probability of to be female was 55/100 =0.55 Probability to be male was 45/100 = 0.45What is the probability of the next three deliveries are females?