In a class of 10 student, probability of exactly I students passing an examination is directly proportional to `i^(2).` Then answer the following questions: If a students selected at random is found to have passed the examination, then the probability that he was the only student who has passed the examination isA. `1//3025`B. `1//605`C. `1//275`D. `1//121`

In a class of 10 student, probability of exactly I students passing an

1.	In a class of 10 student, probability of exactly I students passing an examination is directly proportional to `i^(2).` Then answer the following questions: If a students selected at random is found to have passed the examination, then the probability that he was the only student who has passed the examination isA. `1//3025`B. `1//605`C. `1//275`D. `1//121`
Answer» Correct Answer - A Let P(i) be the probability that exactly I students are passing an examination. Now given that `P(A_(i))=lamda_(i)^(2)(where lamda"is constant")` `impliesunderset(i-1)overset(10)sumP(A_(i))=underset(i-1)overset(10)sum lamdai^(2)=lamda(10xx11xx21)/(6)=lamdaxx386=1` `implieslamda =1//358=5//77.` Let A reprsent the event that selected students have passed the examination. Therefore, `P(A)underset(i-1)overset(10)sumP(A//A_(i))P(A_(i))` `=underset(i-1)overset(10)sum(i)/(10)(i^(2))/(358)` `=(1)/(3850)underset(i-1)overset(10)sumi^(3` `=(10^(2)xx11^(2))/(4xx3850)=11/14` Now ` P(A_(i)//A)=((PA//A_(i))P(A_(i)))/(P(A))` `=(1/358xx1/10)/(11/14)` `=(1)/(11xx55)xx1/5=1/3025`

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