Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that
(a) you both enter the same section?
(b) you both enter the different sections?

Solution:

My friend and I are among the 100 students.

Total number of ways of selecting 2 students out of 100 students = ¹⁰⁰C₂ (Using combinations)

(a) The two of us will enter the same section if both of us are among 40 students or among 60 students.

Therefore,

Number of ways in which we both enter the same section = ⁴⁰C₂ + ⁶⁰C₂

Hence,

The probability that both of us enter the same section,

P (A) = (⁴⁰C₂ + ⁶⁰C₂) / ¹⁰⁰C₂

= [(40)!/(2)!(40 - 2)! + (60)!/(2)!(60 - 2)!] / [(100)!/(2)!(100 - 2)!]

= [40 × 39 × (38)!/2 × (38)! + 60 × 59 × (58)!/2 × (58)!] / [100 × 99 × (98)!/2 × (98)!]

= [(20 × 39) + (30 × 59)] / [50 × 99]

= (780 + 1770)/4950

= 2550/4950

= 17/33

(b) Probability that both of us enter the different sections,

P (B) = 1 - P ( A)

P (B) = 1 - 17/33

= 16/33

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NCERT Solutions Class 11 Maths Chapter 16 Exercise ME Question 5

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (a) you both enter the same section? (b) you both enter the different sections?

Summary:

The probability that (a) you both enter the same section is 17/33 (b) you both enter the different sections is 16/33