### Video Transcript

So it is given. And this doubt that we have to get the probability of getting precisely four hats and no more than four hats when six coins are toast. So this is a motion about the been normal probability. So first of all get ‘s remember what is been normal probability let ‘s say an is the count of test N. P. Is the probability of success and X. Is the count of success. so Q. Is the probable tough failure. So the been normal distribution. So this is an x times poverty X times Q to poverty and minus X. This is the problem. sol when we just come back to our motion the The end the number of trial here is six coins. That means the end is six. And the probability of getting had which is one health 0.5 And the probability of getting not had. That means getting fag end which is besides 0.5. And what about ten. so for share I the ax is equal to four. So we have to get the probable two adam. Is peer to four which is uh 64 combination times This is 0.5 to the exponent four times 0.5 to the world power to therefore 62 combination which is um that is six factorial divided by four factorial, times two factorial and times one over to the department four times one over to the department to Which is equal to that is 15 times 1/16 times 1/4 which is equal to 15/64. That is the answer for the first separate And what about the second gear part ? So it says not more than four hats. That means the probable to actually is not more than four hats means X is less than or peer to four. So that means that is peer to X is equal to zero, plus X is peer to one. Plus up to Actually is equal to four. so in order to fair calculate each of them, we can use the T. I calculator. So you know, see the F officiate just I ‘m just fine to answer here. So I ‘m equitable pressed about in second and distribution there is you know CDF So the number of test here is six. Okay we fair put the trial six MP which is 0.5. so getting had that is 0.5 and come up the X value here so that is X less than or adequate to four. therefore four is included. I ‘m gon na precisely put in four and compress enter. So the probability here is which is 0.89 that is the answer for the second part

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