WEBVTT
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okay for this problem? Part A. We want
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the probability of being given a. It's going to
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be equal to the probability of a Intersect. Be
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divided by the probability of A, which is going
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to be equal to 0.25 divided by 0.5 just going
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to be itself 0.5 Part B. We want the
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probability of not to be given a well. We
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know that the probability of be given a and the
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probability of not be given a need to add upto
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one. You'll have either the MasterCard or not have
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the MasterCard 100% chance of that being true. So
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we can actually calculate this as one minus the probability
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of be given okay, which is going to be
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equal then to 0.5. Since we know that there's
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a 50% chance of you having the MasterCard given that
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you have a visa. Next, we want the
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probability of a given B, which is going to
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be the probability of a Intersect be divided by the
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probability of B, which in this case going to
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be 0.25 divided by 0.4, which comes out to
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moment here 0.5 divided by 0.4 Oh, sorry,
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0.25 provided by 0.4. She comes out, too
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, then 0.6 to 5. And similarly, we
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want the probability of not a given be. It's
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going to be one minus the probability of be given
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a sorry one, minus the probability of a given
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be rather equal to one minus 0.65 which is equal
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to 0.375 Lastly, we want to find the probability
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of a given that we have at least one card
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. So the probability that we have card A,
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given that we have at least one card that is
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going to be probability of the intersection of a and
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one card or one plus card, I'll say,
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divided by the probability of one plus card. So
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we need to figure out what those two probabilities are
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. Well, the probability of a Intersect. Actually
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, it'll be easier to figure out the probability of
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one plus card first. So the probability of having
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at least one card is going to be the probability
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that we have one card or that we have a
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visa and not a MasterCard, that we have a
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MasterCard and not a Visa or that we have a
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Visa and MasterCard. So that's going to be the
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probability of be prime, given a plus. The
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probability of a prime given B plus the probability of
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a Intersect be, Um oh, actually, I
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need to make a slight adjustment here because we want
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these to be rather the intersections, not the givens
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be prime and a or a prime and be or
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A and B. We don't have those intersections given
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as probabilities, but we can calculate them pretty easily
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using Be prime, given a times the probability of
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a plus the probability of a prime given B times
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the probability of B plus. We do have the
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probability of a Intersect B, which is 0.25 So
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putting everything together be prime given A with zero point
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. So we'll have 0.5 times 0.5 plus. That's
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going to be 0.375 times ability of be used four
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plus 0.25 It's going to be so that totals up
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to 0.65 Now, the probability of the intersection of
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having a having a visa. And we have at
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least one card. Well, that No, actually
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, that's not an f. All right? The
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the of A and one plus card. What are
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the different possible ways we could have that Either we
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have a visa and no MasterCard or we have a
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Visa and MasterCard. So that is going to be
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the probability of be prime intersect. A plus probability
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of a Intersect be which is going to be so
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be prime intersect A was what this was here.
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So that's going to be 0.25 plus 0.25 ups,
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not 0.50 point 25 So that is going to be
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0.5 now, putting all of this together probability that
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we have a and at least one card was 0.5
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on the top 0.5 divided by we had 0.65 on
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the bottom. So that is going to give us
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a 0.5. Divided by 0.65 is going to give
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us 0.769 Approximate