WEBVTT
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Suppose that π΄ and π΅ are events with probabilities: probability of π΄ is 0.63 and probability of π΅ is 0.77.
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Given that the probability of π΅ given π΄ is equal to 0.88, find the probability of π΄ given π΅.
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We can find the probability of π΄ given π΅ using a formula.
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We can use the formula the probability of π΄ given π΅ is equal to the probability of π΅ given π΄ times the probability of π΄ divided by the probability of π΅.
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Or we could use the formula the probability of π΄ given π΅ is equal to the probability of π΄ and π΅ divided by the probability of π΅.
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Notice, however, in this second formula, we have the probability of π΄ and π΅.
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In a sample space, here will be event π΄ and here will be event π΅.
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Where π΄ and π΅ overlap would be the intersection of π΄ and π΅.
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So the probability of π΄ and π΅ would be inside of here.
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But looking at what weβre given, we are given the probability of π΄, the probability of π΅, and the probability of π΅ given that π΄ has already happened.
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And all three of those are found here in this formula.
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So this is what weβll use.
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The probability of π΅ given π΄ is 0.88.
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The probability of π΄ is 0.63.
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And the probability of π΅ is 0.77.
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Multiplying on the numerator, we get 0.5544.
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And now we need to divide by 0.77.
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And we get 0.72.
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So this means that the probability of π΄ happening given that π΅ has already happened is 0.72.