WEBVTT
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all right, we have two identical pumps which are
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numbered number one and number two. We're given that
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the probability that both of them fail is 0.1 and
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the probability that either of them fail 0.7 and we're
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supposed to find the probability that one of them fails
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on its own. So they give us some variables
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up here, but quite honestly, we don't need
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them to solve this problem. Instead, I'm going
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to set some variables for some events. So let
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a equal the event at pump number one fails.
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And let's set b to be the event at pump
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number two fails. All right, well, we
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have our addition rule. So the probability of a
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union be because the probability of a plus the probability
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of B minus the probability of a Intersection B.
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So let's think about this in context. A Union
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B is the event that both are sorry. A
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Union B is the event that either of these happened
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either pump one fails or pumped to fails. Well
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, that's this over here. In addition, we
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have a intersection B, which means that they both
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fail at the same time remember, Union refers to
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just the addition of these two events. What happens
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if either of them happened or both happen while intersection
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is limited to exclusively what happens between those two events
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? So we have our minus 0.1 over here and
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keep in mind, Pump number one and pump number
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two are identical, so it's fair to assume that
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the probability they fail is the same. Therefore,
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since we need to find the probability that Pump one
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fails, we could just say Hey p of a
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equals p a V. So there we go.
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Now we do some algebra. We add 0.1 to
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both sides and then divide both sides by two.
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There we go. The probability of pump number one
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failing. It's 0.4 or 4%.