1let s be the set of integers x such that x=a^3+b^3+c^3-3abc,for some integers a,b,c.prove that if x,y are included in s,then xy is included in s
p is the probability that a man aged x years will die in a year.find the probability that out of n men A1,A2,.......,An
each aged x years,A1 will die in a year and will be first to die.
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9 Answers
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21consider the 2 degree polynomial with integer coefficients P(x) = a+ bx + cx2
so x= P(1)P(w)P(w2)
and y = Q(1)Q(w)Q(w2)
so xy can be written as G(1)G(w)G(w2) where G(x) = P(x)Q(x)
degree of G(x) is atmost 4
we can write G(x) = (x3 - 1)A(x) + R(X) degree of R(x) is atmost 2
so G(x) - R(x) has roots as 1,w,w2
so xy can be written as R(1) R(w) R(w2)
so its included
391)
p/n
prob that he will die in a year is p
and prob that he will be first to die is 1/n
so prob that he will die ina year and will be first to die is p/n
341an easy way to test whether this answer is correct is to see what happens if p>1/n.
The number of people who die in that year is not n, so the prob of A1 being the first is not 1/n
71@kunl ,,
Yaar statements bhi copy.!! :P (for 'reviving this')
Lagta hai main famous ho gaya hoo!! :P
1suppose k people die , probability of this is nCkpk(1-p)n-k
you want A1 to be among them , probability of this is n-1Ck-1nCk
among that p that A1 dies first is 1/k
so ans = Σ nCkpk(1-p)n-kkn1k = 1/n ?