00:01
Hello students, our question is let x represent the difference between the number of heads and the number of tells when a coin is toast 46 times.
00:11
Then we have to find out the probability when x is equals to 6.
00:18
Let's solve this.
00:23
So let x represent the difference between the number of and the number of tells when a coin is 40 .5.
00:51
Times and let h is the number of heads and t is the number of tells so from the given information we have h plus t that is equals to 46 that the difference between the number of heads and the number of tells is 40 okay and the h minus t difference of it is 12 this is given to us equation one and equation two now, when we solve this both equation from here, so when we take h minus t first, so this will be h plus t is equal to 40 and h minus t is equal to 12 when we solve this, this will be cancelled out and this will be 2h is equals to 50.
01:50
So from here the value of h will be 26 and from here when we put the value of edge in this an equation so the value of t will be 14.
02:02
This is when we took h minus t if we tag like this h plus t is equals to 40 and t minus h is equal to 12 so when we solve this from here the edge and h will be cancelled out so t is equal to again 52 so from here the value of t will be 26 and the value of h will be 14 okay so clearly we get this two things or either this or this now, if you have to find out the probability getting 26 height and 14 tells.
02:55
So this will be 40.
02:57
See, we will do the combination her.
02:59
So this is 40, 6, c 26 and half and its power is 26 and half and its power is 14.
03:10
And that is equals to when we solve this, this will be 40 c 26 and half and its power is 14.
03:21
So this will be 0 .0211.
03:24
Now if you see probability of getting 14 hats and 26 tells so this will be this will be the opposite of that that is 40 c 14 half and its power is 14 because the probability is half really and half and its power is 26.
03:45
So this will be equals to 14 c 14 half and its power is 14.
03:53
So this will be equals to 14 c 14.
03:53
So so when we solve this, this will be 0 .0211 .021.
04:01
That will be the same.
04:02
So the total probability of getting difference between number of x and number of tells that is equal to probability of x is equal to.
04:33
So when we solve this, this will be 0 .211 plus 0.
04:37
Point sorry 0 .021 plus 0 .0211 so when we solve this is the 0 .0 422 this is our answer so this is a probability of x is equal to 12 an x is equal to okay similarly as our problem from the given information we can write down h plus t is equal to 46 and modulus of h minus t is equal to 10 this is equation 1 this is equation 2.
05:13
And when we solve, again when we saw equation 1 and 2, this will be h plus t is equal to 46...