NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 41
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 41
A bag has 24 balls: \(x\) red, \(2x\) white, \(3x\) blue. One ball drawn. Find probability it is (i) not red (ii) white.
Answer:
(i) \(\dfrac{5}{6}\), (ii) \(\dfrac{1}{3}\)
Detailed Answer with Explanation:
Step 1: Write total balls in terms of \(x\).
Total = red + white + blue = \(x + 2x + 3x = 6x\).
We are told total = 24, so:
\(6x = 24\)
\(x = 4\)
Step 2: Find actual numbers of each colour.
- Red balls = \(x = 4\)
- White balls = \(2x = 8\)
- Blue balls = \(3x = 12\)
Total check: \(4 + 8 + 12 = 24\) ✔
Step 3: Recall probability formula.
Probability = \(\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}}\)
Total outcomes = 24 (since there are 24 balls).
Step 4: (i) Probability of not red.
‘Not red’ means either white or blue.
Number of not red balls = white + blue = \(8 + 12 = 20\).
So, probability = \(\dfrac{20}{24} = \dfrac{5}{6}\).
Step 5: (ii) Probability of white.
Number of white balls = 8.
So, probability = \(\dfrac{8}{24} = \dfrac{1}{3}\).