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01 Apr 2013, 01:18
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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?
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01 Apr 2013, 09:56
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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!
01 Apr 2013, 21:26
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Find the number of people who are alive at the end of day 4 and then subtract that from the beginning amount.
So at end of day 0, there are x people.
Therefore, there are 3x/4 people at the end of day 1.
And (3x/4) * (3/4) at the end of day 2. >>> 9x/16
And (9x/16) * (3/4) at the end of day 3. >>> 27x/64
And (27x/64) * (3/4) at the end of day 4. >>> 81x/256
So x - (81x/256) is the number of people who died by the end of day 4.
Which is (256x/256) - (81x/256) = (175x/256).
And so, the answer is 175/256, which can be broken down into prime factors: (5^2)(7) / 2^8. So, the answer can't be simplified further.
So at end of day 0, there are x people.
Therefore, there are 3x/4 people at the end of day 1.
And (3x/4) * (3/4) at the end of day 2. >>> 9x/16
And (9x/16) * (3/4) at the end of day 3. >>> 27x/64
And (27x/64) * (3/4) at the end of day 4. >>> 81x/256
So x - (81x/256) is the number of people who died by the end of day 4.
Which is (256x/256) - (81x/256) = (175x/256).
And so, the answer is 175/256, which can be broken down into prime factors: (5^2)(7) / 2^8. So, the answer can't be simplified further.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
