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

a. 4/23

b. 6/23

c. 8/23

d. 17/23

**Solution:**

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that

Total number of students n(S) = 23

Number of students in houses A, B and C = 4 + 8 + 5 = 17

Here the remaining students = 23 - 17 = 6

n (E) = 6

Probability that the selected student is not from A, B and C is

P (E) = Favourable outcomes/ Total outcomes

Substituting the values

= 6/23

Therefore, the probability that the selected student is not from A, B and C is 6/23.

**✦ Try This: **A school has five houses A, B, C, D and E. A class has 52 students, 5 from house A, 10 from house B, 6 from house C, 3 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from B, C and D is

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 14

**NCERT Exemplar Class 10 Maths Exercise 13.1 ****Problem 26**

## A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is a. 4/23, b. 6/23, c. 8/23, d. 17/23

**Summary:**

A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is 6/23

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