Question Video: Calculating Conditional Probability given the Probability of Both Events Occuring Mathematics

For events 𝐴 and 𝐵, where 𝑃(𝐴 ∩ 𝐵) = 0.3 and the 𝑃(𝐵) = 0.8, calculate the probability of event 𝐴 occurring given that event 𝐵 has occurred.

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Video Transcript

For events 𝐴 and 𝐵, where the probability of 𝐴 intersection 𝐵 is 0.3 and the probability of 𝐵 is 0.8, calculate the probability of event 𝐴 occurring given that event 𝐵 has occurred.

This question is dealing with conditional probability. We recall that the probability of 𝐴 given 𝐵 is equal to the probability of 𝐴 intersection 𝐵 divided by the probability of 𝐵. The vertical line means given that. This is the probability of 𝐴 occurring given that 𝐵 has occurred. The symbol that looks like a lowercase n means the intersection. This is the probability that both 𝐴 and 𝐵 occur.

We are told that the probability of 𝐴 intersection 𝐵 is 0.3 and the probability of 𝐵 is 0.8. The probability of 𝐴 given 𝐵 is, therefore, equal to 0.3 divided by 0.8. This is equal to 0.375. We could also have written as the fraction three-eighths in its simplest form.

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