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:
The probability that exactly 5 students passing an examination is

Options

A. `1//11`
B. `5//77`
C. `25//77`
D. `10//77`

Answer

B

Explanation

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`