WEBVTT
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okay for this problem. We have that 40% of
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people on vacation use their laptops. And actually I'll
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yeah, I'll leave that as Event A is using
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their sorry, 40% of people use their emails.
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You have 30% of people use their cell phones,
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labeling that as B and way have that 25% of
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people use their laptops, so that is events.
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See also, given that of the or other that
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there's 23% chance of somebody thio use their email actually
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labeled email. This is cell. This is laptop
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probability of somebody using their email and their laptop equal
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to 0.23 Probability of somebody not using any of the
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list of devices. A not and be not and
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see not or not, is equal to 0.51 of
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the probability that a given C is equal to 0.88
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Probability of C given B is equal to 0.7.
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So for our first question here, A. We
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want the probability of be given a that's probability of
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using cell phone given that they used in their email
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that is equal to the probability of B and C
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divided by the probability of C which itself is equal
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to the probability. Oh, sorry, the B
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and C N N b and A. Yeah,
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which is are divided by probability of a, which
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is equal to the probability of A and B divided
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by the probability of a just changing it. So
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we have it in the exact form we had it
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up there. They're the exact same. That's 0.23
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divided by 0.4 comes out to 0.575 part B want
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. The probability of be given see is equal to
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the probability of B and C divided by the probability
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of C equal to the probability of C given b
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times the probability of B divided by the probability of
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C where we know the probability of c given b
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so that is 0.7 times 0.3 divided by 0.25 which
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comes out to 0.84 for C. You have We
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want to find the probability of B given A and
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C so this one is a little bit trickier.
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What we want to do here This is actually where
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we use that knowledge that 51% of people don't use
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any of their devices. So that means that probability
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of somebody using A or B or C is equal
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to one minus 0.51 equals 0.49 So we also and
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this is in the textbook. It's in the believe
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it's in the axioms and interpretations section. Um,
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yeah, it's in the axioms and interpretation section of
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the textbook. In the version that I have here
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. It's about Paige, 37 or actually page 13
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. Rather, um, but we have that The
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probability of A or B or C is equal to
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the probability of a plus probability of B plus probability
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of C minus probability of a and B minus the
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probability of a and see minus the probability of B
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and see, plus the probability of A and B
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and C. So the reason why I'm going off
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on this is actually that probability of A and B
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and C right there, because probability of be given
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A and C is the same thing as the probability
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of A and B and see divided by the probability
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of I believe it should be it's divided by the
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probability of Excuse me. It is divided by the
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probability of A and C so we can use this
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formula down here to get the probability of A and
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B and C plug it in up there and we
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already have the probability or a probability of A and
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C is easy to get probability of A and C
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people, to the probability of a given see which
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we have and the probability of C, which we
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also have So rearranging this equation we end up getting
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that s o rearranging this equation and dividing by a
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given see times. PFC basically substituting in mhm rearranging
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this equation for p of A and B N c
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substituting into the p of be given A and C
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equation. If the probability of be given A and
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C is equal to 0.49 minus p of a minus
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p of B minus p of C plus p of
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and now with the A and C things. So
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I believe we have the probability of A and C
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no, we don't not explicitly given so probability of
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A and C we can write as the probability of
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I'm sorry, probably of A and B. We
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have So leave that in that form than probability of
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a and see we don't have. We can write
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that as probability of a given see times the probability
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of C the probability of a or Serie B N
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c then going to be, plus the probability of
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C given b times probability of being now. Last
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thing is that divide everything their i p of a
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given see as PSC so going through and substituting in
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all of our numbers here should get 0.49 minus 0.4
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, minus 0.3 minus 0.25 plus 0.23 I'm sorry.
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0.23 plus 0.8 eight 10 0.25 plus 0.7 times 0.3
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all divided by 0.88 I'm 0.25 which is going to
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equal once we go through and throw that into a
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calculator. 0.909