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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 6 · Set 1 · Q38
"Eight Ball" is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and white. Of the 15 numbered balls,…
"Eight Ball" is a game played on a pool table with $\displaystyle 15$ balls numbered $\displaystyle 1$ to $\displaystyle 15$ and a "cue ball" that is solid and white. Of the $\displaystyle 15$ numbered balls, eight are solid (non-white) coloured and numbered $\displaystyle 1$ to $\displaystyle 8$ and seven are striped balls numbered $\displaystyle 9$ to 15.
The $\displaystyle 15$ numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random. Based on the above information, answer the following questions :
(i)
What is the probability that the drawn ball bears number $\displaystyle 8$ ?
(ii)
What is the probability that the drawn ball bears an even number ?
OR What is the probability that the drawn ball bears a number, which is a multiple of $\displaystyle 3$ ?
(iii)
What is the probability that the drawn ball is a solid coloured and bears an even number?
Marking-scheme solution
(i) P (drawing ball bearing number $\displaystyle 8$ ) \(\displaystyle =\frac{1}{15}\)
(ii) Even numbers \(\displaystyle =2,4,6,8,10,12,14\)
No. of favourable outcomes \(\displaystyle =7\)
\(\displaystyle P(\) even number ball \(\displaystyle )=\frac{7}{15}\)
OR
(ii) Multiples of $\displaystyle 3$ are $\displaystyle 3$, $\displaystyle 6$, $\displaystyle 9$, $\displaystyle 12$, $\displaystyle 15$
No. of favourable outcomes = $\displaystyle 5$
\[\therefore \mathrm{P}(\text { multiple of } 3)=\frac{5}{15}=\frac{1}{3}
\]
(iii)
Solid colour and even number $\displaystyle 2$, $\displaystyle 4$, $\displaystyle 6$, $\displaystyle 8$
\[\mathrm{P}(\text { solid colour and bear an even no. })=\frac{4}{15}
\]
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.