### Video Transcript

For two independents events π΄ and π΅, where the probability of π΄ is 0.2 and the probability of π΅ is 0.3, calculate the probability of π΄ given π΅.

The vertical line in our question means βgiven that.β We need to calculate the probability of π΄ given that π΅ happens. The probability of π΄ given π΅ is equal to the probability of π΄ intersection π΅ divided by the probability of π΅. We are also told in the question that our events π΄ and π΅ are independent. We recall that for independent events, the probability of π΄ intersection π΅ is equal to the probability of π΄ multiplied by the probability of π΅.

As the probability of π΄ is 0.2 and the probability of π΅ is 0.3, the probability of π΄ intersection π΅ is, therefore, equal to 0.2 multiplied by 0.3. This is equal to 0.06. We can now calculate the probability of π΄ given π΅. This will be equal to 0.06 divided by 0.3. This is equal to 0.2.

Therefore, the probability of π΄ given π΅ is 0.2.