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Question Video: Calculating the Conditional Probability of Two Independent Events Mathematics • 10th Grade

For two independents events ๐ด and ๐ต, where ๐‘ƒ(๐ด) = 0.2 and ๐‘ƒ(๐ต) = 0.3, calculate ๐‘ƒ(๐ด/๐ต).

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Video Transcript

For two independents events ๐ด and ๐ต, where the probability of ๐ด is 0.2 and the probability of ๐ต is 0.3, calculate the probability of ๐ด given ๐ต.

The vertical line in our question means โ€œgiven that.โ€ We need to calculate the probability of ๐ด given that ๐ต happens. The probability of ๐ด given ๐ต is equal to the probability of ๐ด intersection ๐ต divided by the probability of ๐ต. We are also told in the question that our events ๐ด and ๐ต are independent. We recall that for independent events, the probability of ๐ด intersection ๐ต is equal to the probability of ๐ด multiplied by the probability of ๐ต.

As the probability of ๐ด is 0.2 and the probability of ๐ต is 0.3, the probability of ๐ด intersection ๐ต is, therefore, equal to 0.2 multiplied by 0.3. This is equal to 0.06. We can now calculate the probability of ๐ด given ๐ต. This will be equal to 0.06 divided by 0.3. This is equal to 0.2.

Therefore, the probability of ๐ด given ๐ต is 0.2.

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