Statistics for Programmers-Table of Contents
The probability that event A will occur under the condition that event B will occur is called the conditional probability.
It can be calculated by the following formula.
Conditional probability = Probability of A and B occurring / Probability of B occurring
P(A|B) = \frac{P(A∩B)}{P(B)}
Shake the dice twice to calculate the probability that the sum of the rolls will be 8 or more. However, "4" will always appear the first time.
In this case, the following equation holds.
Conditional probability= \frac{(1st time is 4∩ 1st time and 2nd time is 8)}{The first time is 4}
The probability of becoming 4 the first time is
\frac{1}{6}
is.
The probability that the first time is 4 and the total of the first time and the second time is 8
Since it is calculated by the probability of becoming 4 x the probability of getting any of 4,5,6, it can be calculated by the following formula.
\frac{1}{12} = \frac{1}{6}\times\frac{3}{6}
Applying these to the formula I wrote at the beginning,
\frac{1}{2} = \frac{\frac{1}{12}}{\frac{1}{6}}
The answer is 1/2.
In other words, the conditional probability of this example is 50%.
Event A and Event B are said to be "independent" when Event B does not affect Event A, even if there is a condition that Event B occurs.
P(A|B) = P(A)
If event A does not occur when event B occurs, then event A and event B are said to be "exclusions".
P(A|B) = 0
The multiplication theorem is a transformation of the formula for obtaining conditional probabilities as follows.
P(A∩B) = P(A) \times P(A|B)
Suppose you have 10 lots and 4 wins. After Mr. A wins, Mr. B draws a lottery. What is the probability that both Mr. A and Mr. B will win?
Probability of hitting Mr. A= \frac{4}{10}
Probability of hitting Mr. B= \frac{3}{9}
So the answer is 2/15.
\frac{2}{15} = \frac{4}{10} \times \frac{3}{9}
-What is conditional probability
Recommended Posts