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A coin is flipped 8 times. Assume that the coin is fair (that is, all outcomes are equally likely). What is the probability that the number of heads is different from the number of tails?
$n|S|=2^8$
Help me with this problem... please
asked May 5, 2018 at 17:48
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The outcome of the experiment is described by a binomial distribution, with $n=8$ ($n$ is the number of trials), $p=\frac{1}{2}$ (the probability of getting an head), and $X$ is the number of heads.
Of course, you have the same number of heads and tails when $X=4$. This event occurs probability:
$$P(X = 4) = {8 \choose 4}\left(\frac{1}{2}\right)^4\left(1-\frac{1}{2}\right)^{8-4} = \frac{70}{256}$$
Therefore, the probability that the number of tails and heads is different is just:
$$1 - P(X=4) = \frac{186}{256} \simeq 0.73.$$
answered May 5, 2018 at 17:59
the_candymanthe_candyman
13.4k4 gold badges33 silver badges60 bronze badges
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We can recognize a random variable $X$ follows the binomial law $\mathcal B(8,\frac12)$ and you look for
$$\Bbb P(X\ne4)=1-\Bbb P(X=4)=1-{8\choose4}\left(\frac12\right)^{4}\left(\frac12\right)^{8-4}=1-{8\choose4}\left(\frac12\right)^{8}$$
answered May 5, 2018 at 17:56
user296113user296113
7,49913 silver badges30 bronze badges
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Video Transcript
Hi am that bit and i'm going to him. He answering your question now. I'M moping up your question here in the question. Here we are going to discuss about the binomial distribution. Let me remind you that if we have, the accident follows by the binomial in the n and the b and then the probability the x equal to k will equal to n to k, p power, k and then times 1 minus p power n minus k in The question here we flip the factors 8 times, so we have the x here equal to the number of attending a hat, and then it will follow by the binomial, with the n equal to 8 and the p the probabitgetting, a hat equal to the 0.5 point. Now in the question, i want to find the probability that we'll get on the town so means that will equal to the 0 had. And if we apply the formula here, we will have the 820 and then the .50. Then 1 minus 0.5 per 0. And i will compute, we get the answer equal to 39 red to the farther simal places and for the question b want to find a probability had so x, equal to the 8. And then we have the 8 to 8. And then we have the 15 power. 810 times 1 minus upon 5 power, 8 minus 8 point, and if we compare again the same thing as the question i and for question c, when you find a probability that is 1 hat sum, is that x will be greater equal to 1. So far this probability it would be easier to consider the compliment. 1 minus the brome equal to 0 then x, to the 0 equal to the answer. In the part i equal to 39. It then we'll get the answer equal to 19961, and that will be the answer for your question.
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