11

Part of 2006 Stanford Mathematics Tournament

Problems(2)

A Black and White View on Insurance

Source:

An insurance company believes that people can be divided into 2 classes: those who are accident prone and those who are not. Their statistics show that an accident prone person will have an accident in a yearly period with probability 0.4, whereas this probability is 0.2 for the other kind. Given that 30% of people are accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy?

2006 SMT Team Round #11 - Determine Sum of Roots

Source:

P(x)=c_{2006}x^{2006}+c_{2005}x^{2005}+\ldots+c_1x+c_0

r_1,r_2,\ldots,r_{2006}

. The coefficients satisfy

2i\tfrac{c_i}{c_{2006}-i}=2j\tfrac{c_j}{c_{2006}-j}

for all pairs of integers

0\le i,j\le2006

\sum_{i\ne j,i=1,j=1}^{2006} \tfrac{r_i}{r_j}=42

\sum_{i=1}^{2006} (r_1+r_2+\ldots+r_{2006})

algebrapolynomial