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Probability
NCERT Exemplar Ch 13
CBSE_NCERT_EXEMPLAR_CH13
Grade 10
Question:
A box contains $12$ balls out of which $x$ are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If $6$ more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find $x$.
Step-by-Step Solution
Key Concept: Initially $P_1 = \dfrac{x}{12}$. After adding 6 black balls: total $= 18$, black $= x + 6 \Rightarrow P_2 = \dfrac{x+6}{18}$. Set $P_2 = 2 P_1$.
Stepwise Solution:
Initial probability of black ball $P_1 = \dfrac{x}{12}$. [0.5 Mark]
New total balls $= 12 + 6 = 18$. New black balls $= x + 6$. New probability $P_2 = \dfrac{x + 6}{18}$. [1.0 Mark]
$\dfrac{x + 6}{18} = \dfrac{x}{6} \Rightarrow x + 6 = 3x \Rightarrow 2x = 6 \Rightarrow x = 3$. Value of $x$ is $3$. [1.0 Mark]
Marking Scheme:
• Initial probability $P_1 = x/12$: 0.5 Mark • New probability $P_2 = (x+6)/18$: 1.0 Mark • Setting equation $(x+6)/18 = 2(x/12)$: 0.5 Mark • Solving for $x = 3$: 1.0 Mark
Correct Answer:
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