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September 1st, 2013, 10:34 AM   #1
Neb
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Help required in solving question

The question that's torturing me, is the following:

"Some boys and girls, more specific n boys and n girls, are at a camp. Every night, each boys gives a kiss to one randomly chosen girl. So do the girls.
One of the teenagers however is infected with a contagious virus. You get infected with the virus if you kiss the person who's already infected.
Once you're infected with the virus, the day after you're contagious too.
Now, p_i is the probability that a random teenager is infected after spending i nights at the camp (thus, p_0 = 1/(2*n)).
(a) determine p_1
(b) prove: p_(i+1) = 2 * p_i - (p_i)^2 if i >= 1"

I sincerely hope someone could help me with this question.

Ben
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