GIVEN:
Prize has to be given to two teachers from six teachers present on the stage in which one teacher is sports teacher
FORMULA:
Probability of sports teacher not receiving the prize = 1 – (probability of sports teacher receiving the prize)
CALCULATION:
Total number of ways prize can be given to any two teachers from 6 teachers =
6C2 =
= 15
Probability of sports teacher receiving the prize:
Two persons receiving the prize one (sports teacher) is fixed. The second person can be selected from remaining 5 teachers in 5 ways.
Thus, probability =
=
Probability of sports teacher not receiving the prize = 1 – (probability of sports teacher receiving the prize)
= 1 –
() =
∴ Sports teacher not getting the prize
Alternate Method:
Total number of ways prize can be given to any two teachers from 6 teachers =
6C2 =
= 15
Total number of ways sports teacher not getting the prize =
5C2 = 10
∴ Required probability =
=