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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.
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This question is dealing with conditional probability.
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We recall that the probability of 𝐴 given 𝐵 is equal to the probability of 𝐴 intersection 𝐵 divided by the probability of 𝐵.
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The vertical line means given that.
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This is the probability of 𝐴 occurring given that 𝐵 has occurred.
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The symbol that looks like a lowercase n means the intersection.
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This is the probability that both 𝐴 and 𝐵 occur.
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We are told that the probability of 𝐴 intersection 𝐵 is 0.3 and the probability of 𝐵 is 0.8.
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The probability of 𝐴 given 𝐵 is, therefore, equal to 0.3 divided by 0.8.
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This is equal to 0.375.
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We could also have written as the fraction three-eighths in its simplest form.