Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is

Let the number of students failing be $$k$$.

Since a student fails if marks are less than $$50$$, in the worst case assume each failing student gets exactly $$49$$ marks.

The average marks of $$7$$ students is $$62$$.

Hence, total marks

$$=7\times62=434$$

Variance is $$20$$, so

$$\sum (x_i-62)^2=7\times20=140$$

For each failing student,

$$x_i=49$$

Therefore,

$$ (49-62)^2=169 $$

If $$k$$ students fail, then

$$169k\le140$$

Hence,

$$k\le\frac{140}{169}<1$$

Therefore, the maximum possible number of students who can fail is

$$\boxed{0}$$