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You toss coin 2,0(0) times It comes "p heads 1100 and tails 900. Can JYou claim that the coin is fair? Justify Your answer:...

Question

You toss coin 2,0(0) times It comes "p heads 1100 and tails 900. Can JYou claim that the coin is fair? Justify Your answer:

You toss coin 2,0(0) times It comes "p heads 1100 and tails 900. Can JYou claim that the coin is fair? Justify Your answer:



Answers

A fair coin is tossed $2 n$ times. Probubility of getting more heads than tails is (a) $1 / 2$ (b) ${ }^{2 n} C_{n}\left(\frac{1}{2}\right)^{2 n}$ (c) $1-2^{\prime \prime} C_{n}\left(\frac{1}{2}\right)^{2 n}$ (d) $\frac{1}{2}-{ }^{2 n} C_{n}\left(\frac{1}{2}\right)^{2 n+1}$

Your point is an for if hatch, the number of outcomes that result in heads satisfies the condition more, less off pitch minus 50 by five. This cryonic will do one points of school fight. No, we need to describe the number off outcomes that did your mind. And I'm fair point that distrust 100 times. We know that if morning was presidency, it's solution ist you list on minus C or your residency. So really, I didn't given any while a deviation. Right. This is hatch minus 15 by fight less than or equal to minus 1.64 Fight off hedge minus 50 by fight. But I don't know what it will do. One point since four fight Let us simplify this inequality. First, multiply both sides off the inequality by five. We get five times so which minus 50 by fight listen are equal to five times off minus one point 64 fine. One simplifying this we get hedge minus 50 is less than or equal to minus a point toe. Do Frank now and both sides off this inequality by 50. We get much this lesson already well too. What the 1.77 freight. Now let us simplify this inequality. Multiply both sides off this inequality by fine Get fine time. So much. Minus 50 by finest girl money 25 to 1.6 for free. Simplifying this we get hedge minus 50 is greater than or equal to a point toe fight. I hold sight's off this inequality by 50 we get Hutch, you know, not equal to be a going toe. Do fight. Hence the number of outcomes that determined. And a fair point that this just 100 times will be anxious. Zito to 41 union every night since the daughter Logan. Miss Andre. So the number of workers that determined and for coin that isjust 100 times this hatch is equal to 0 41 union 5900.

Really 1 21 were flipping the coins and they had this formula H minus 50 divided by by five. Greater than or equal to 1.6, or I and I guess that chest me. It's an unfair coin. If the heads is up in that Well, I really like it. Unfair. That would be interesting. What could you put on it? I guess you could make the head be heavier. Maybe you could put a bunch of fingernail polish on it, weighted down. And this is a great tour. It's an or so. Basically, we just take that opposite sign opposite number. So I want to multiply all three sides by five. So can undo the division. And this side plans five to undo the division hand. Let's see, you're going to this simplified one, and I get hh minus 50. I know. Forgive me if I don't do that. Long education. Punch it in my hand. And his 6.1 point 645 plans 58.22 Farm in a negative. A 0.225 You know, it looks like I'm gonna be added 50 adding this dean to both sides and then that gets the age is greater than 58 to 25 where h is less than or equal to 41 0 to hear that drop my calculator. 41 1 went 775 You can't do part of the toss. It's just the way life iss. So age would have to be greater than equal to 59 or age is less than equal to 41. And so, if we do this in interval notation design interval notation on this one, I guess it doesn't say, does it? Okay, then. So we're not gonna do it. What is gonna leave it like that? There you go.

86 we flip a coin 100 times and note that it only comes up hedge 20% of the time. The meanest entered aviation for the number of times the coin lands on heads is mu equals 20 and standard deviation Sigma equals four soft. The following a. There is about a 68% chance that the number of heads will be somewhere between blank and blank. 68 represents one standard deviation s o. We're gonna just add and subtract one standard deviation. So our answer for this would be 16 for the first blank 24 for the second, and B There's about a 95% chance that the number of heads would be somewhere between 12 and 28. We know this because these values represents our mean, which is 20 with two standard deviations added subtracted from it. And then lastly, there's about a 99.7% chance, which is what represents three center deviations. That it will be somewhere between eight and 32. Again eight and 32 is actually what you get when you take three standard deviations away from the mean and Adam to the mean

You guys in this problem? We're told that we put the coin 1000 times and out of those 1000 times, it landed heads 5500 and 26 times and were asked to solve for the experimental probability of landing heads and the experimental probability of landing tales. Experimental probability is different from theoretical probability, as you might have guessed And, uh, we're being asked are experimental probability cause the problem gives us an experiment. It gives us that we flipped 1000 times and without we landed heads 5526 times. So in order to determine Ph, what we need to do is we need to divide the number of experimental times that we landed heads over than over. And of s the number of times we flipped the coin well, the number of total of total times we flipped the coin were given that we flipped it 1000 times. So that's 1000 and the number of times we landed. Heads were given that as well. So 526. So the probability of us ah, of us probability The experimental probability of lending heads is 0.5 to 6, and that is gonna be equal to P of each. Now we're going to solve for the other probability problem. The other probability that were asked to solve for is the experimental probability off P of tea. Now, be of Ty's gonna be similar to PVH. We're going to basically do the same steps. We're gonna have to find the number of times it landed tails and then divide that by the total number of flips, the total number flips. Who we know is all is I's not gonna change. It's still 1000. And now we need to find out the number of times it landed a number of times it landed tails. Now, if you flip the coin, it'll either lands, heads or tails. So if it landed head 526 times, that means that landed tails 1000 minus 526 times. And 1000 minus 526 is 500 74. So the number of times that the coin landed tails in the 1000 flips is 500 is 500 is whoops. Sorry about my math right here. This is actually 474 uh, 474. And so the number of times the coin landed tails is 474 times out of the 1000 flips. So P of T s o the N f t. The number of times Atlanta tales is 4 74 which makes our probability 0.474 for the experimental probability of landing tails.


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