00:01
Hi, i'm david and i'm here to have you and send your question.
00:04
Now let me bring up your question here.
00:07
In this question we want to throw a fair con until you have two hat consecutively and want to find the expected number of the throws.
00:17
Now we know that the probability of the hat is equal to the proper player in the tail and because it means a fair cone will be equal to 0 .5.
00:27
Now if we call the x, it will be equal to the number of the throw.
00:33
Need it to get two hat consecutively and now want to find the e on the x now to find the e on the x i'm going to condition on the first throw now it will be e on the x given then the first throw we obtained with the hat and then because conditional we need to times perp but pretty time the hat and then plus the second option will be the first throw again the tail and then times proper pellitum the tail.
01:10
Now the proper political head equals 0 .5, proper building the tail equals equal to 1 5 as well.
01:18
Now if we get the first one will be the head and then we want to have the next one will be the head and then it will be we will consider on the second option so we will have here we will condition one more time so it will equal to the e .m.
01:38
The x given that the first one will be the head and now we will continue on the second throw even the head and then time the 0 .5 plus let me move on out little this is going to be the 0 .5 here now and then we will continue on the second throw that the second throw will be the tail then times 0 .5 we do the same thing on the second option here so let me move the 0 .5 out here and then we will have now with because it the first one will be the the tail so it means that we will start over from the beginning of the game so we will but we only throw one so we have one plus e on the x and then we start over and this will be the e on the x on the left hand side now the next step because we obtained the hat 2 consecutive times so this one will be e equal to 2 and then times under 0 .5 plus now because we obtain the second will be the tail so we have to start over the game so means that we will have the 2 already we up and we throw 2 times already plus e on the x and then times with the 0 .5 everything here will times with the 0 .5 out there and then we will have this one will be plus now we will have, we multiply 0 .5 inside, we have 0 .5 plus 0 .5 e on the x...