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Current time:0:00Total duration:3:23

Using probabilities to make fair decisions example

CCSS.Math:

Video transcript

- [Instructor] We're told that Miguel and Jordan decide to roll a pair of fair six-sided dice to determine who has to vacuum their apartment. If the sum is seven, then Miguel will vacuum. If the sum is three or four, then Jordan will vacuum. If the sum is anything else, they'll roll again. Is this a fair way to decide who vacuums? Why or why not? So pause this video and see if you can figure that out. All right, now let's work through this together. So let's just think about all of the different outcomes of a fair six-sided die. And then which of those outcomes result in Miguel vacuuming? Which of those results or those outcomes result in Jordan vacuuming? And then which of them, I guess we would have to roll again? So let me do it this way. I will make six columns, one, two, three, four, five, and six, and I'll make six rows, one, two, three, four, five, and then let's see, one, two, three, four, five. Let me do one more, and six, just like that. And so if I have, this is dice one, this is dice two. Dice one could be a one, two, three, four, five, or six. Dice two could be a one, two, three, four, five, or six. Now let's think about the sums of these rolls here. So this one will be two, three, four, five, six, seven. This would be three, four, five, six, seven, eight. This one over here is going to be four, five, six, seven, eight, nine. This is five, six, seven, eight, nine, 10. This is six, seven, eight, nine, 10, 11. And then seven, eight, nine, 10, 11, or 12. Now let's think about all the scenarios where Miguel will vacuum. That's where the sum is seven. So we can see, this is Miguel here, one, two, three, four, five, six. So six out of the total of 36 outcomes result in Miguel vacuuming. So this is a six out of 36 probability, or this is equal to 1/6, at least on that first roll. Then, if we think about Jordan vacuuming, the sum is three or four. So that is one, two, three, four, five, six, seven. So this is a 7/36 probability. So there's a higher probability based on this little game they're doing that Jordan will be picked on any given roll. Now, there's all of these other outcomes where they'll roll again, but every time they roll again, there's a higher probability that Jordan will be picked than Miguel will be picked. So, no, this is not fair. This is, let's see, if we look at all the choices, no, there's a higher probability that Jordan vacuums. Yep, that does seem to be the case.