WEBVTT
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All right, So we're given an inventory of shirts
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. Some of them were shortly. Some are long
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. See, some are small, medium large sum
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are plaid printer stripe. We're giving the distribution in
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this table here and were asked a bunch of probability
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questions about this inventory. But before we do that
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, I'm gonna do something real quick just to make
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my life a little easier in solving this problem.
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I'm gonna write in a total call him in a
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total row, both of these tables as such.
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Now let's start with the short sleeves and small rope
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. In order, find the total for this row
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. Ijust add everything up in the road. So
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four plus two of six six plus five is 11
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. So this is 0.11 and we'll continue going down
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the line. So let's see. This is eight
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and seven, which is 15 15 and 12.
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It's 27 and this is that's 10 18. Now
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what these distributions mean these numbers are the distribution of
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small, medium and large short sleeve shirts, respectively
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. I'm going to do the same thing down here
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with the columns now. So plaid, we have
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four plus 8 12 Totals 5 15 2799 and seven
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At 16 eight and 12 2025 25. We're also
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gonna fill in this bottom right hand corner here.
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We're just gonna add up either the total rose or
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the total column. It doesn't matter. Basically,
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this will give us the distribution of all shorts T
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shirts. All right, We're just gonna add these
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three because 15 and 25 is a nice 40.
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We can add 16 to that rather easily. That's
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56. This should be the same as thes numbers
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Here. You can check that for years. I'm
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gonna do the same thing down here. So this
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adds up to 0.8 This adds up to 0.22 This
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adds up to 0.14 It adds up to 0.170 point
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09 0.18 The shadow add up 0.44 Yes, and
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something we should also check real quick is these two
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numbers they add up to one. And this should
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make sense because the percentage of short sleeve shirts puts
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the percentage Long sleeve shirt should be ah, 100%
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of the shirts. Which is this one, all
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right. With that in mind, let's start solving
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these problems. Our first problem. We're supposed to
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find the probability of selecting a medium long print shirt
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. It's rather simple. We can just look in
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the table long sleeves, medium print and that 0.5
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all right, probability of a medium print in general
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. Well, we just add the probability of finding
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medium print shortly, plus a medium print long sleep
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. So that will be here. I'm just going
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to color code them waas 0.5 should give us 0.12
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So those are answers apart and be part see were
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given were asked for the probability of selecting a short
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sharp Well, we can't id did that already,
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actually with peace total columns. So there you go
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0.56 Same here with long shirts 0.44 So there are
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answers. Alternatively, you could add up everything inside
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here, but like I've established, that's already the
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same of is what we did here. We just
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added less terms. All right. Number four are
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part D. I should say we need to find
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the probability of just selecting a medium certain. General
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. Here's where these total columns will come in handy
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. All right, let's look at short sleeve.
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The total distribution of medium shortly shirts 0.27 As for
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long seeds, 0.22 So this illegal 0.27 0.22 which
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is 0.49 All right. As for the prince will
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do the same thing. We'll look in the print
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for the short sleeves. 0.16 the prince for long
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sleeves 0.9 sarah 0.16 plus 0.9 equal 0.25 All right
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, here we have some conditional probabilities content with male
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. We need to find the probability of a selectee
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and medium short given that it was short and plaid
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. Now, your reminder that probability is defined as
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the number of successful outcomes over the number of total
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outcomes in this case are successful. Outcomes are the
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medium shirts within the subset and our total outcomes are
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all the short sleeved plaid shirts. So that would
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be this column of the table right here now.
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Of those the mediums All right here. So in
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our numerator will have 0.8 in our denominator will have
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0.15 This equals 0.533 rounding to three decimal places finally
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part off. So we need to find the probability
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of finding a short sleeve shirt, given that it
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was a medium and plaid shirt. Once again,
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successes over over total outcomes. So our successes,
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our short sleeve medium plaid shirts, which are right
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here. So that goes in the numerous up?
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Yeah. No, that's great. So that goes
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in the numerator. My fault. I thought I
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was circling something else. That's our total welcomes.
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We would just add our medium plaid shorts T shirts
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with our medium plaid long sleeve shirts. So we're
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gonna throw that nominator. Uh, hurray for color
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coding. So this equals 0.8 over 0.18 This is
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equal to this Reduces down to eight for ninth.
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So that 0.4443 decimal places and what we could use
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a similar role. Similar methodology down here. Well
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, since we only have two conditions outside of the
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medium and plaid shorts lever long sihf, you know
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that the probability of getting a long sleeve shirt,
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giving them medium. Platt is one minus. The
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probability of not getting a long sleep start given medium
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and Platt or the probability of finding a short sleeve
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shirt giving that it's medium in plaid. And since
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we've already found that very conveniently, you could just
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subtract that out 0.5 by six and there you go
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.