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If a student copies his assignments from his friend he would get 80 marks. If he had done the assignments independently he would have scored 50 marks out of 100 and if the teacher finds he is cheating he will be penalized and will be given 0 marks. The probability that the teacher catches his cheating is 0.3. If he copies 10 such assignments, what is the probability that he will lose more marks with copying than by doing his independent work independently?

I'm a tad bit unsure,but still my approach would be as below:- :)

The experiment is conducted 10 times,and we need to consider the cases and add up those cases in which he gets less than (50*10=500,if he gives the exam fairly),and maximum before 500  is when he cheats and remains uncaught for 6 times out of 10,which makes his score (80*6=480).

Now,let's assume p be the probability he cheats and succeeds in that,(p=1-0.3=0.7) ,and probability of failure be (q=0.3),now it's just adding up the binomial terms for which number of success<=6,I'll create a table below:-

Success Marks Probability
6 80*6=480 $\binom{10}{6}(0.7)^{6}0.3^{4}$
5 80*5=400 $\binom{10}{5}(0.7)^{5}0.3^{5}$
4 80*4=320 $\binom{10}{4}(0.7)^{4}0.3^{6}$
3 80*3=240 $\binom{10}{3}(0.7)^{3}0.3^{7}$
2 80*2=160 $\binom{10}{2}(0.7)^{2}0.3^{8}$
1 80*1=80 $\binom{10}{1}(0.7)^{1}0.3^{9}$
0 80*0=0 $\binom{10}{0}(0.7)^{0}0.3^{10}$

Summing up the above binomial probability terms will yield the ans

answered ago by Junior (849 points)
selected ago
0

Here, no negative marking. right??

what is meaning of loosing more marks??

He could either get 0  or 80 in copying.

right??

+1

suppose there is only 1 assignment

if he copy and do not get caught = 80 marks.

if he tries to copy and found cheating he gets 0 marks.

if he does it own his own he gets 50 marks.

$\therefore$ he will lose more marks with copying(if he gets caught) i.e. he loses 80 marks

than by doing his independent work independently i.e. he loses only 80-50 = 30 marks if he does on his own instead of copying.

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Yup, exactly.. :)
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suppose he gets 7 success.

then we need to consider the 3 cases right ?

if he copy and do not get caught = 240 marks.

if he tries to copy and found cheating he gets 0 marks.

if he does it own his own he gets 150 marks.

ā“

he will lose more marks with copying(if he gets caught) i.e. he loses 240 marks

than by doing his independent work independently i.e. he loses only 240-150 = 90 marks if he does on his own instead of copying.

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Actually question is ambiguous.
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@Satbir

If he gets 7 success ,assuming success means he cheats successfully,he gets (80*7=560)marks , we just need to consider this case...as success means cheating without getting caught. But, here the question asks to cite out those cases in which he scores less if he cheats........there can be atmost 6 success if we need to satisfy that constraint(score(cheating)<500(fairplay in all the 10 assignments)).

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Please explain why 7 success cheating successfully will not be included in detail.
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if he cheats successfully in 7 cases....then for each of those case he gets 80 marks,totaling to (80*7=560)...but according to the question we only need to find probability for those cases where he scores less if he cheats,than if he gives exam independently,if he gives 10 exams independently,he scores 50 for each of those 10 exams,resulting in (50*10=500 marks)....80*7 becomes greater than 500,and hence we shouldn't' consider those cases in which he scores greater than 500...

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@Debdeep1998

here cheats and caught or not, that also matters

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yup,both caught and not caught has been captured in the binomial term......it's a bernoulli trial actually with 2 possible scenarios, either caught or not caught..
+1
Suppose

Among 10

2 done independently.

1 cheated and not caught.

and 7 other also cheated and caught.

Do u consideded this case?
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Umm....Nope I didn't do that.......It has been mentioned in the question that "If he copies 10 such assignments" which means that he had copied 10 assignments,so he didn't do 2 independently among the 10... š
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ok, yes

But I cannot get, where he is copying and losing? rather I can see he is copying and gaining marks for.

How he could copying and losing more marks??

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Copying and losing as in, like had he done it independently he would have got more marks.So, like if he gets 6 successes, so he gets 80*6=480 marks and gets caught for remaining 4 and gets 0 marks,had he done all of them independently,he would have got 500 marks.Comparing both the cases, he lost (500-480=20 marks )because he cheated. Relatively he's losing actually.

So,yaa I admit that the question framing is kindda difficult to understand,it could have been much more clearer...  :D