score780 wrote:

One fourth of a group of infected people will die everyday due to a virus. What fraction of this group would be expected to be killed after 4 days?

suppose the number of people in the start is T

people dying on 1st day = (1/4)*T= T/4

people left = 3T/4

on, 2nd day the number of people dying = (1/4)(3/4)T = (3/16)T

no of people left = (9/16)T

on, 3rd day the number of people dying = (1/4)(9/16)T = (9/64)T

no. of people left = (27/64) T

on, 4th day the number of people dying = (1/4)(27/64)T = (27/256)T

no. of people left = (81/256) T

Probability of number of people killed in 4days = total killed in 4days/ total number of people in the starting = ((T/4) + (3T/16) + (9T/64) + (27T/64) )/ T

= (1/4) + (3/16) + (9/64) + (27/256) = (64 + 16*3 + 4*9 + 27)/256 = (64+48+36+27) /256 = 175/256

hope it helps!

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ankit

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