5

IFor a binomial experiment with a n-8 trials, each with success probability P-0. '15, what is the probability of = obtaining less than 5 successes?Mour answer:...

Question

IFor a binomial experiment with a n-8 trials, each with success probability P-0. '15, what is the probability of = obtaining less than 5 successes?Mour answer:0.5330.9370,0620.7644805{790665

IFor a binomial experiment with a n-8 trials, each with success probability P-0. '15, what is the probability of = obtaining less than 5 successes? Mour answer: 0.533 0.937 0,062 0.764 4805 {79 0665



Answers

Binomial Trials Five independent trials of a binomial
experiment with probability of success $p=0.7$ are performed.
Find the probability of each event.
At least three successes

Okay, so we've got binomial experiment with five intimate and trials. The probability of success is 0.7. And so we're going to calculate what is the probability when we have no successes. So then we're going to have five Choose zero, which is going to look exactly like this. You're a factorial five factorial. And so then this is just going to be one, and then we're gonna have 0.7 to the zeroth power, which is again, just gonna be one, and then we'll have a 0.3 to the fifth. So once we calculate with point three to the fifth is it's going to be this very small number 0.0 0243 We've got our answer.

Okay, so we want this probability of at least 26 ass is, and so I'm going to go about the method that I mentioned earlier where I'm actually going. Well, actually, I am going to go with. So then one way we could do this is we could find the probability of exactly zero fill. Success isn't exactly one successes. We could subtract that from woollen. Or since we already have a lot of the information here already, we can just go ahead and add the one part that we don't have, which the one part we don't have right now is exactly two successes. So for exactly two successes, we've got five. Choose to times 0.7 squared times 0.3 squared. Sorry, cubed. And then we'll be kind of going along this list. Do, do, do, do, do do do do do do do do support. Seven. Q no 70.3 square you did it to do. This is really maybe not entirely no cereal to go all the way through. But just for the heck and pain of it will finally have a plus five. Choose five 2.7 to 50 0.3 cubed, which which I'm only sorry, that should be 20 And the only reason I'm saying go with this method is because we already know what this is. This is 0.83692 So we have to do here is find what this number is. So let's go ahead and find out what this number is. First off, this is gonna be 10 so we'll have 10 times 100.7 squared, which will be a 0.49 and then 0.3 cubed. It's gonna be 0.27 So let's go ahead and we'll find that out. That's gonna be come plus R zero point 83692 is gonna give us 0.969 to 2

So we're looking for the probability of this binomial experiment with five independent trials with probability success of 0.7 and we're looking for the probability that we have all successes. So we're gonna have 5 to 5, which is going to just be this, which is just gonna be one. And we'll have 0.7 to the fifth and 0.3 to the zeroth power, which is again just one. So we'll do 0.7 to the fifth, which is equal to zero point 16 807

Okay, so this is a fun one. So this is saying at most one failure, which is exactly the same as saying at least four successes, which we've actually already done in a previous problem. So you can refer back to the that problem as well. But so what we're doing here and we're going to say five choose four for success is that way. We only have one failure. That's gonna be 0.7 to the fourth with 0.3 plus five. That drill this is five two's five here. I just like writing it out, because to me, it's a little bit more intuitive and helps me remember exactly what I'm doing and where I'm pulling numbers from. And so then from previous problem, I actually already know this calculation. And just so you know, this is going to end up equaling. This is gonna simplify to five. This is going to simplify the one this is going to simplify toe one just so that we can kind of go back through and see how some of this simplifies a little bit. But once you do all this man arithmetic here, you'll end up getting zero point 52 disc disc, we'll end up meaning 0.5 to 8 to 2. This is supposed to be a two.


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