91Ó°ÊÓ

A school contains in grades 1,2,3,4,5, and 6. Grades 2,3,4,5 or 6 all contain the same number of students, but there is twice this number in grade 1.

Let the number of student in the each grades 2,3,4,5 or 6 is m and the number of student in grade 1 is 2m.

The total number of students is 7m.

The number of students in odd grades (i.e, number of students in grade 1, grade 3, and grade 5) is 4m.

Here, we need to select 1 student from the odds grade and 1 student from a total number of students.

The probability of a randomly selected student from a list of all the students is in odds grade is –

\(\begin{array}{c}\Pr \left( {{\rm{Selected}}\,{\rm{student}}\,{\rm{is}}\,\,{\rm{in}}\,{\rm{odds}}\,\,{\rm{grade}}} \right) = \frac{{{\bf{Number}}\,{\bf{of}}\,{\bf{Favourable}}\,{\bf{outcomes}}}}{{{\bf{Total}}\,{\bf{outcomes}}}}\\ = \frac{{{}^{4m}{C_1}}}{{{}^{7m}{C_1}}}\\ = \frac{{\frac{{4m!}}{{1! \times \left( {4m - 1} \right)!}}}}{{\frac{{7m!}}{{1! \times \left( {7m - 1} \right)!}}}}\\ = \frac{{4m}}{{7m}}\\ = \frac{4}{7}\\ = 0.571429\end{array}\)

Thus, the probability of a randomly selected student in odds grade is 0.571429