Video: Calculating the Conditional Probability of Two Independent Events

For two independents events 𝐴 and 𝐡, where 𝑃(𝐴) = 0.2 and 𝑃(𝐡) = 0.3, calculate 𝑃(𝐴/𝐡).

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Video Transcript

For two independents events 𝐴 and 𝐡, where the probability of 𝐴 is 0.2 and the probability of 𝐡 is 0.3, calculate the probability of 𝐴 given 𝐡.

The vertical line in our question means β€œgiven that.” We need to calculate the probability of 𝐴 given that 𝐡 happens. The probability of 𝐴 given 𝐡 is equal to the probability of 𝐴 intersection 𝐡 divided by the probability of 𝐡. We are also told in the question that our events 𝐴 and 𝐡 are independent. We recall that for independent events, the probability of 𝐴 intersection 𝐡 is equal to the probability of 𝐴 multiplied by the probability of 𝐡.

As the probability of 𝐴 is 0.2 and the probability of 𝐡 is 0.3, the probability of 𝐴 intersection 𝐡 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 𝐡. This will be equal to 0.06 divided by 0.3. This is equal to 0.2.

Therefore, the probability of 𝐴 given 𝐡 is 0.2.

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