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# (a) In Example $1.10,$ identify three events that are mutually exclusive.(b) Suppose there is no outcome common to all three of the events $A, B$ , and $C .$ Are these three events necessarily mutually exclusive? If your answer is yes, explain why; if your answer is no, give a counterexample using the experiment of Example $1.10 .$

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### Video Transcript

all right. Inquest number 12 were supposed to go back into the reading example 1.10 and then by three events that are mutually exclusive. Okay, so, um, if you remember back to that example there, um, three different car dealerships and, for instance, like GM czar, our Chevys and camel axe, the user, Chryslers or Buicks, Dodges and Fords are on whatever the two are. But the idea is mutually exclusive. Events do not have any common members near them, so they're they don't overlap. Okay, so if you buy a car nearby, afford or you buying a GM not buying boats. So for GM, those two events, our mutual, it's mutually exclusive. You own exclusive. Um, but then so are GM and Chrysler Eisler. Um, and so are you. Those would be the three usually exclusive. That's, um Now then, be is not really clear as to what is actually asking. Says suppose there is no outcome. Comment? All three of the events A, B and C by these three events necessarily mutually exclusive. Um, if you're, um, answers. Yes. Explain why your answer's no counter itself. So, um, I don't believe they're actually talking about these three events being a B A C. Because A, B and C in this case specific case are mutually exclusive, and there's nothing common all free. But in general, if you talk about any three events, a B C. We could have no common events to all three, but you could have events there commented to. Okay, so this would be example of a diagram right here where these two and be would not be mutually exclusive, but there is no common, um, event that's in both a B s. You're some butter and A and B, but they're not in also see. So that's one way to explain question number 12.

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