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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 1 · Set 1 · Q37
BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant…
BINGO is game of chance. The host has $\displaystyle 75$ balls numbered $\displaystyle 1$ through 75. Each player has a BINGO card with some numbers written on it.
The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where $\displaystyle 48$ balls were used before Tara said 'BINGO'.
Based on the above information, answer the following :
| Numbers announced | Number of times |
| $\displaystyle 0$-$\displaystyle 15$ | $\displaystyle 8$ |
| $\displaystyle 15$-$\displaystyle 30$ | $\displaystyle 9$ |
| $\displaystyle 30$-$\displaystyle 45$ | $\displaystyle 10$ |
| $\displaystyle 45$-$\displaystyle 60$ | $\displaystyle 12$ |
| $\displaystyle 60$-$\displaystyle 75$ | $\displaystyle 9$ |
(i)
Write the median class.
(ii)
When first ball was picked up, what was the probability of calling out an even number ?
(iii)
(a)
Find median of the given data.
OR
(b)
Find mode of the given data.
Marking-scheme solution
| Number announced | $\displaystyle 0$-$\displaystyle 15$ | $\displaystyle 15$-$\displaystyle 30$ | $\displaystyle 30$-$\displaystyle 45$ | $\displaystyle 45$-$\displaystyle 60$ | $\displaystyle 60$-$\displaystyle 75$ |
| Number of times $\displaystyle (f)$ | $\displaystyle 8$ | $\displaystyle 9$ | $\displaystyle 10$ | $\displaystyle 12$ | $\displaystyle 9$ |
| $\displaystyle c f$ | $\displaystyle 8$ | $\displaystyle 17$ | $\displaystyle 27$ | $\displaystyle 39$ | $\displaystyle 48=\mathrm{N}$ |
(i)
$\displaystyle \frac{N}{2}=24$
∴ median class is $\displaystyle 30$-$\displaystyle 45$
(ii)
$\displaystyle \mathrm{P}$ (picking up an even number) $\displaystyle =\frac{37}{75}$
(iii)
\[\text { (a) } \begin{aligned}
\text { Median } & =30+\frac{\left(\dfrac{48}{2}-17\right)}{10} \times 15 \\
& =40.5
\end{aligned}
\]
OR
(iii)(b)
Modal class is $\displaystyle 45$-$\displaystyle 60$
\[\begin{aligned}
\text { Mode } & =45+\frac{12-10}{2 \times 12-10-9} \times 15 \\
& =51
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.