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 grade 3 is m

Here, we need to select 1 student from grade 3 and 1 student from total number of students.

The probability of a randomly selected student from a list of all the students is in grade 3 is

\(\begin{aligned}{}\Pr \left( {{\rm{Selected}}\,{\rm{student}}\,{\rm{in}}\,{\rm{grade}}\,3} \right) &= \frac{{{\bf{Number}}\,{\bf{of}}\,{\bf{Favourable}}\,{\bf{outcomes}}}}{{{\bf{Total}}\,{\bf{outcomes}}}}\\ &= \frac{{{}^m{C_1}}}{{{}^{7m}{C_1}}}\\ &= \frac{{\frac{{m!}}{{1! \times \left( {m - 1} \right)!}}}}{{\frac{{7m!}}{{1! \times \left( {7m - 1} \right)!}}}}\\ &= \frac{m}{{7m}}\\ &= \frac{1}{7}\\ &= 0.142857\end{aligned}\)

Thus, the probability of a randomly selected student in grade 3 is 0.142857