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CCSS.Math: , - [Instructor] We're
told that Maya and Doug are finalists in a crafting competition. For the final round,
each of them spin a wheel to determine what star material
must be in their craft. Maya and Doug both want to get
silk as their star material. Maya will spin first, followed by Doug. What is the probability that
neither contestant gets silk? Pause this video and think
through this on your own before we work through this together. All right, so first let's think
about what they're asking. They want to figure out the
probability that neither gets silk, so I'm gonna
write this in shorthand. So I'm going to use MNS for Maya no silk. And we're also thinking about Doug not being able to pick silk. So Maya no silk and Doug no silk. So we know that this could be viewed as the probability that
Maya doesn't get silk. She, after all does get
to spin this wheel first, and then we can multiply that by the probability that
Doug doesn't get silk, Doug no silk, given that
Maya did not get silk. Maya no silk. Now it's important to think
about whether Doug's probability is independent or dependent on
whether Maya got silk or not. So let's remember Maya will
spin first, but it's not like if she picks silk, that somehow silk is taken out of the running. In fact, no matter what she picks, it's not taken out of the running. Doug will then spin it again. And so these are really
two independent events, and so the probability
that Doug doesn't get silk given that Maya doesn't get silk, this is going to be the same thing as the probability that
just Doug doesn't get silk. It doesn't matter what happens to Maya. And so what are each of these? Well, this is all going to be equal to the probability that
Maya does not get silk. There's six pieces or six options of this wheel right over here. Five of them entail her not
getting silk on her spin. So five over six. And then similarly, when
Doug goes to spin this wheel there are six possibilities. Five of them are showing
that he does not get silk, Doug no silk. So times 5/6, which is of
course going to be equal to 25/36, and we're done.

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