NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question 37

Question. 37

A child’s game has 8 triangles (3 blue, 5 red) and 10 squares (6 blue, 4 red). One piece is lost at random. Find the probability it is (i) a triangle (ii) a square (iii) a blue square (iv) a red triangle.

Answer:

(i) \(\dfrac{4}{9}\), (ii) \(\dfrac{5}{9}\), (iii) \(\dfrac{1}{3}\), (iv) \(\dfrac{5}{18}\)

Detailed Answer with Explanation:

Step 1: Write down the given information.

  • Triangles: 8 in total (3 blue + 5 red)
  • Squares: 10 in total (6 blue + 4 red)

Total pieces = 8 + 10 = 18.

Step 2: Recall probability formula.

Probability of an event = \( \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).

(i) Probability of a triangle

Number of triangles = 8. Total pieces = 18.

So, \( P(\text{triangle}) = \dfrac{8}{18} = \dfrac{4}{9} \).

(ii) Probability of a square

Number of squares = 10. Total pieces = 18.

So, \( P(\text{square}) = \dfrac{10}{18} = \dfrac{5}{9} \).

(iii) Probability of a blue square

Number of blue squares = 6. Total pieces = 18.

So, \( P(\text{blue square}) = \dfrac{6}{18} = \dfrac{1}{3} \).

(iv) Probability of a red triangle

Number of red triangles = 5. Total pieces = 18.

So, \( P(\text{red triangle}) = \dfrac{5}{18} \).

Final Answer:

(i) \(\dfrac{4}{9}\), (ii) \(\dfrac{5}{9}\), (iii) \(\dfrac{1}{3}\), (iv) \(\dfrac{5}{18}\).

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