Tossing 7 coins simultaneously and observe the number of...

Tossing 7 coins simultaneously and observe the number of heads. a) is this a binomial experiment? Your answer (enter Y or N) --> b) what is the value for n? Your answer --> c) can x be 0? Your answer (Y or N) --> d) can x be 8? Your answer (Y or N) --> e) what is value for p? Your answer --> f) how many different ways to get 4 heads? Your answer --> g) find P(x=5). Answer must be with 5 decimal places. Your answer -->

Transcript

00:01 In this question, we look at a bag, right? suppose in the bag you have three coins.

00:04 You have the copper coin, and you have the gold coin, and you also have the silver coin.

00:10 Now, when you flipped, the probability coin will come ahead is 0 .3 for copper, and 0 .5 for gold, 0 .7 for silver, right? now imagine you are going to flip this coin 10 times.

00:26 You'll ask what's probability you are going to get and a hat, right? what's probability you're going to get an hat after talking 10 times? well, the probability, of course, is given by, you know, first, it's the first, this probability you get a copper coin, right? so that's actually one third chance, right? so you need divided by one third for copper.

00:49 And also the one third for gold and one third for cfr according to question, right? so there's, you have, you have one third chance to get a copper or a gold or a, civil coin.

01:01 So, and then if you get a copper coin, the probability you're going to get 10 hats is given, of course, given by 0 .3 to the part of n times 1 minus 3 .0 .7 to the part of 0 .7 to the part of 10 minus and right.

01:18 And multiplied by, you know, the factor of 10 over the factor of n and 10 minus an factor, right? now, this fact, these factors that was test, you know, gives you the number of ways, you're likely to, the number of ways you can get n heights, right? and then of course, if you get a golden coin, then the property will become 0 .5 to the part of n and times 0 .5 to the part of 10 minus n, and you have 10 to the, again, the same factor, right? exactly the same factor anyway.

01:55 And also, if you get a silver coin, they probably can 0 .7 to the point, of n and multiply 0 .3 to the power of 10 minus n and times 10 factor over n factor and 10 minus n factor, right? so that would be the exact expression for this probability.

02:15 Now you ask you to calculate a few values, right? first of all you say n equals 0.

02:22 So you don't talk.

02:23 You don't, you don't know what is the probability for this? you don't, and you don't, n equals 0 that means sorry you don't let me an equals that mean you get 0 at heads right and you're just plugging n into the expressions you find this one third and equals zero zero zero right so this is a one right and this will be of course 0 .7 to the power of 10 right so and you'll find and actually this is of course all of this number of ways being one right so you basically get 0 0 .7 to part of 10 to part of 10 plus also 0 .5 to the part of 10 plus 0 .3 to the power of 10, right? so that would be your probability.

03:03 And you'll find this, of course, to be very small, you'll find this to be given by 0 .7 to the to the power of 10, and then you're plus 0 .5 to the part of 10.

03:19 And you know that this is an extremely small number, and plus 0 .3 to the power of 10.

03:27 And i found this, and you divided by three, and you found this to be actually very small...

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