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Mathematical probability problem! ultrahard
Generation 1: extinction probability =p, survival probability = 1- p, and survival quantity = 2 (1-p);

Second generation: extinction probability = 2( 1-p)p, survival probability = 2 (1-p) (1-p) = 2 (1-p)? Survival = 2*2( 1-p)? =2? ( 1-p)? ;

Generation 3: extinction probability = 2*2( 1-p)? p=2? ( 1-p)? P, survival probability =2? ( 1-p)? ( 1-p)=2? ( 1-p)? Survival = 2*2? ( 1-p)? =2? ( 1-p)? ;

Generation 4: Extinction probability = 2*2? ( 1-p)? p=2? ( 1-p)? P, survival probability = 2? ( 1-p)? ( 1-p)=2? (1-p) 4. Survival =2*2? ( 1-p)^4=2^4( 1-p)^4;

Generation n: extinction probability = [2 (n-1)] * [(1-p) (n-1)] * p, survival probability = [2 (n-1)] * [(65433)

If p is set to 0.5( 1/2), the problem is easy to understand. (and p= 1/2 is the key point).

P= 1/2, then, after one hour, half will be extinct, and the surviving half will be split in two, with the same number as before; Another hour passed, and it was still the same; Because 2n (1-p) n = 2n * (1/2) n =1.

When p≥ 1/2, these viruses will never be completely extinct.

When P < 1/2, this group of viruses will gradually decrease and eventually become extinct.