Conditional Probability Formula
In the mathematics, conditional probability is defined as one of the most important topics
. For the calculation of conditional probability one of the important formula is used. The occurrence of one event with respect to another events is called as the definition of probability. In this, the event A occurred with the knowledge of event B and the event B occurs with the knowledge of event A. In this article, we are going to see about the conditional probability with some worked out problems.
The probability is the experimentations that are repeatedly done under some certain conditions. The results for the one or more experiments are identical. The probability includes the event, trial, sample space.
Every sampling unit has a definite probability of being included in the sample. There are different types of probability sampling. Some of them are 1. Random sampling, 2. Stratified sampling 3. Systematic sampling 4. Multi stage sampling.
Random Sampling: A sample from a population is said to be a random sample if every item of the population has equal chance for being selected. A random sampling is divided into two types. They are Unrestricted random sampling and restricted random sampling. A random sample is said to be unrestricted if every item drawn for the sample is noted and is again replaced into the population before the next item is drawn
Explanation to Conditional Probability Formula
The explanation given for the conditional probability formula is given as follows,
Formula:
Conditional Probability = P(B | A) = '(P(A) and P(B))/(P(A))'
where,
P(A) = Event of A
P(B) = Event of B
P(A) and P(B) = Independent Events
Example Problems to Conditional Probability Formula
Problem 1: A and B be two events, P(B) = '10/75' and P(A and B) = '25/75'
Solution:
Step 1: Given:
A and B = Events
P( A and B ) = '25/75'
P( B ) = '10/75'
Step 2: To find:
P( B | A ) = Conditional Probability
Step 3: Formula:
Conditional Probability = P(B | A) = '(P(A) and P(B))/(P(A))'
Step 3: Solve:
P( B | A ) = '(10/75)/(25/75)'
= '10/75' 'xx' '75/25'
= '10/25'
= '2/5'
Result: Conditional Probability = '2/5'
Thus, this is the required answer for solving the condiional probability using the formula.
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Problem 2: A and B be two events, P(B) = '60/90' and P(A and B) = '30/90'
Solution:
Step 1: Given:
A and B = Events
P( A and B ) = '60/90'
P( B ) = '30/90'
Step 2: To find:
P( B | A ) = Conditional Probability
Step 3: Formula:
Conditional Probability = P(B | A) = '(P(A) and P(B))/(P(A))'
Step 3: Solve:
P( B | A ) = '(60/90)/(30/90)'
= '60/90' 'xx' '90/30'
= '60/30'
= 2
Result: Conditional Probability = 2
Thus, this is the required answer for solving the condiional probability using the formula.
Practice Problems to Conditional Probability Formula
Problem 1: A and B be two events, P(B) = '15/45' and P(A and B) = '30/45'.
Answer: '1/2'
Problem 2: A and B be two events, P(B) = '15/50' and P(A and B) = '30/50'.
Answer: '3/6'
by: nitinp
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