Video Transcript
For two independents events 𝐴 and 𝐵, where the probability of 𝐴 is 0.2 and the probability of 𝐵 is 0.3, calculate the probability of 𝐴 given 𝐵.
The vertical line in our question means “given that.” We need to calculate the probability of 𝐴 given that 𝐵 happens. The probability of 𝐴 given 𝐵 is equal to the probability of 𝐴 intersection 𝐵 divided by the probability of 𝐵. We are also told in the question that our events 𝐴 and 𝐵 are independent. We recall that for independent events, the probability of 𝐴 intersection 𝐵 is equal to the probability of 𝐴 multiplied by the probability of 𝐵.
As the probability of 𝐴 is 0.2 and the probability of 𝐵 is 0.3, the probability of 𝐴 intersection 𝐵 is, therefore, equal to 0.2 multiplied by 0.3. This is equal to 0.06. We can now calculate the probability of 𝐴 given 𝐵. This will be equal to 0.06 divided by 0.3. This is equal to 0.2.
Therefore, the probability of 𝐴 given 𝐵 is 0.2.
