Course Content
Probability Theory Basics
4. Commonly Used Continuous Distributions
5. Covariance and Correlation
Probability Theory Basics
Law of Total Probability
The law of total probability is a fundamental concept in probability theory. This law can be formulated as follows:
Let's provide some explanations:
- We have split our space of elementary events into n different incompatible events.
- We want to calculate the probability of some other event in this space of elementary events.
- We can calculate P(A) using the formula described above.
This law is often used when a stochastic experiment can be divided into different stages, and each stage is stochastic too.
Let's consider an example involving a manufacturing company that produces two types of products: Product 1 and Product 2. The company produces 60%
of Product 1 and 40%
of Product 2. The defect rate for Product 1 is 10%
, while the defect rate for Product 2 is 5%
.
We want to calculate the probability of randomly selecting a defective product from the company's inventory.
In this example:
Event A: Selecting a defective product.
Partition events: H₁ = Selecting Product 1, H₂ = Selecting Product 2.
Now we can use the law of total probability to solve this task:
You have two baskets: the first one contains 3 cats' toys and 7 dog's (10 toys), the second one contains 12 cat's toys and 8 dog's (20 toys). The probability to choose the first basket is 0.4, and to choose second is 0.6. Calculate the probability to get cats' toy.
Select the correct answer
Everything was clear?