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Probability
NCERT Exemplar Ch 13
CBSE_NCERT_EXEMPLAR_CH13
Grade 10
Question:
A jar contains $24$ marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\dfrac{2}{3}$. Find the number of blue marbles in the jar. If $6$ more blue marbles are added to the jar, find the new probability of drawing a green marble.
Step-by-Step Solution
Key Concept: Let green marbles be $g$. $P(\text{green}) = \dfrac{g}{24} = \dfrac{2}{3} \Rightarrow g = 16$. Blue marbles $= 24 - 16 = 8$. After adding 6 blue marbles: total $= 30$, green remains $16$.
Stepwise Solution:
Let number of green marbles $= g$. Total marbles $= 24$. $P(\text{green}) = \dfrac{g}{24} = \dfrac{2}{3} \Rightarrow 3g = 48 \Rightarrow g = 16$. [1.5 Marks]
Number of blue marbles $= 24 - 16 = 8$. [1.0 Mark]
When $6$ more blue marbles are added: New total marbles $= 24 + 6 = 30$. Number of green marbles remains $16$. [1.0 Mark]
New probability of drawing a green marble $= \dfrac{16}{30} = \dfrac{8}{15}$. [1.5 Marks]
Marking Scheme:
• Finding green marbles $g = 16$: 1.5 Marks • Finding initial blue marbles $= 8$: 1.0 Mark • Finding new total marbles $= 30$: 1.0 Mark • Calculating new green probability $= 8/15$: 1.5 Marks
Correct Answer:
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