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Outside the principal room, there are 5 students of class 11th and 4 students of class 12th. The principal calls 3 students to come inside the room. What will be the probability that out of 3 students, at least 2 students are from class 12th?

Outside the principal room, there are 5 students of class 11th and 4 students of class 12th. The principal calls 3 students to come inside the room. What will be the probability that out of 3 students, at least 2 students are from class 12th? Correct Answer 17/42

GIVEN:

Outside the principal room, there are 5 students of class 11th and 4 students of class 12th.

CONCEPT:

Number of ways to select ‘a’ out of ‘b’ = bCa

Probability = Number of favorable case / Total cases

CALCULATION:

Total students = 5 + 4 = 9

We want ‘out of 3 students, at least 2 are students of class 12th’

2 possibilities are there:

2 students are from class 12th and 1 from class 11th or all 3 students are from class 12th

∴ Required probability = {(5C1 × 4C2) + 4C3}/9C3

⇒ {(5 × 6) + 4}/84

⇒ 34/84

⇒ 17/42

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