A Die is Continuously Rolled Until the Total Sum of All Rolls Exceed
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point) A die is continuously rolled until the total sum of all rolls exceeds 400_ What is the probability that at least 110 rolls are necessary?
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(1 point) A die is continuously rolled until the total sum of all rolls exceeds 400. What is the probability that at least 120 rolls are necessary?
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Video Transcript
Hello there. I see that. You have a question about how a die is continuously road until the total sum of all roles exceeds 400. They want to know what is the probability that at least 120 rolls are necessary. Well to calculate this we might have to do a little something where we have our y where we have. All right. Some Are sigma where we have our 1 20 up top and they're equally in the one. Transact sigh. So then how we go further with the calculation that we do 1 20 times E times X. Y. Equals. So that's supposed to be 20. That's my best. I don't know where I wrote. 181 20 times um In parentheses 1 6 times one plus From 1 to 6 there. and we'll get 3.5 when you do that and you end up getting um for 420. So we saw for the first part. Um And this first part would be for our um for this sign. And then the second part they were going to do our time are few times why? And how we set that up that we do 120 times 1/6 times. You know The 1- This number that we got from the beginning part because we're gonna make it smaller and we're gonna square it. And by doing so you end up getting like 17.5. That's supposed to be a five. Let me fix that because it's supposed to be a five. Okay It would be 120 times 16 times 17.5 is what you get when you um do this type of setup where we get um 350 and then for sigma we're going to square root it. So we square rooted. We get 18.71. So then after that we end up trying to solve our ski C score. Which is why you see x minus um this sign and sigma I mean our standard DVD and sigma. So that's why you see a setup like that. So we place our 1 20 in the parentheses lift one with I mean we Put 4 20 and the princes of 400 And we defied that by 18 points. And then when we get negative 1.07 so that we have a setup. If the x It was great of 400 R c score would be 0.0 point um 14 to 3. And if the x is less than 400 will do one minus zero point 1423. Where we will get And doing this attraction we get 0.857 seven. So and with this part you can um time stop by 100 and we see Yeah I think time's up by 100. Let me make sure that's right. Yeah you times that by 100. So we go down by like two decimal points. So we go like 12 which would give us 85.77% chance um chance that um oops we can conclude that um There's a probability that a 5.77% of the need um of needed um roles um would be um At least 1 20 rolls Um are necessary to exceed um 400 and, yep. That is it. I hope you found this very helpful and please take care sorry and please take care of stay safe. Okay bye.
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