NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question 26

Question.  26

A class has 23 students: 4 from house A, 8 from B, 5 from C, 2 from D and the rest from E. One student is selected at random to be the monitor. The probability that the selected student is not from A, B and C is

(A)

\(\dfrac{4}{23}\)

(B)

\(\dfrac{6}{23}\)

(C)

\(\dfrac{8}{23}\)

(D)

\(\dfrac{17}{23}\)

Detailed Answer with Explanation:

Step 1: Total students in the class

Total = 23 students.

Step 2: Students from each house

  • House A = 4
  • House B = 8
  • House C = 5
  • House D = 2
  • House E = Remaining students

Step 3: Find number of students in House E

Add students from A, B, C, D: \(4 + 8 + 5 + 2 = 19\).

So, House E = Total – (A + B + C + D) = \(23 - 19 = 4\).

Step 4: Which houses are not allowed?

The student should NOT be from A, B, C. That means the student must be from D or E only.

Step 5: Favourable outcomes

Students in D = 2

Students in E = 4

Total favourable = \(2 + 4 = 6\).

Step 6: Probability formula

Probability = (Favourable outcomes) ÷ (Total outcomes)

Probability = \(\dfrac{6}{23}\).

Final Answer: Option B (\(\dfrac{6}{23}\)).

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