Ohh i totally missed that line.
Thanx a lot :)
On Wed, Sep 21, 2011 at 10:46 AM, pankaj agarwal <
agarwal.pankaj.1...@gmail.com> wrote:
> @Nitin Garg
>
> Question 6 -
>
> i agree that greater the sum is and greater the probability to getting it.
> but in given question if sum>100 then rolling is stopped
> so for
>
> P(106)=P(100)*1/6
> P(105)=P(100)*1/6+P(99)*1/6
> .
> .
> .
> P(101)=P(100)*1/6+P(99)*(1/6)+P(98)*(1/6)+P(97)*(1/6)+..+P(95)*(1/6)
>
> now P(101) is more
>
> cleare me if something is wrong.
>
>
>
> On Mon, Sep 19, 2011 at 1:35 PM, Nitin Garg <nitin.garg.i...@gmail.com>wrote:
>
>> Question 6 -
>> Intuitively you can see that the greater the sum is, the greater the
>> favorable events in sample space.
>>
>> e.g. - sum = 1 .. cases {(1)} Pr = 1/6
>> sum = 2 cases {(2),(1,1)} Pr = 1/6 + 1/36
>> sum = 3 cases {(3),(2,1)(1,2)(1,1,1)} Pr = 1/6 + 1/36 +1/36 +
>> 1/216
>>
>>
>> for a more formal proof, look at the recursion -
>>
>>
>> P(k) = (P(k-6) + P(k-5) + P(k-4)... P(k-1)))/6
>>
>> where P(0) = 1, P(i) = 0 for i<0
>>
>> Base case -
>> P(2) > P(1)
>>
>> Hypothesis -
>>
>> P(i) > P(i-1) for all i <= k
>>
>> To prove
>> P(k+1) > P(k)
>>
>> Proof
>> P(k+1) - P(k) = (P(k) - P(k-6))/6 > 0
>>
>>
>>
>
>
>
>> --
>> Pankaj Agarwal
>> Communication and Computer Engineering
>> LNMIIT,jaipur
>>
>> --
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--
Nitin Garg
"Personality can open doors, but only Character can keep them open"
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