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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 1 · Set 1 · Q37
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'. Numbers announced Number of times $\displaystyle 0$-$\displaystyle 15$ $\displaystyle 8$ $\displaystyle 15$-$\displaystyle 30$ $\displaystyle 9$ $\displaystyle 30$-$\displaystyle 45$ $\displaystyle 10$ $\displaystyle 45$-$\displaystyle 60$ $\displaystyle 12$ $\displaystyle 60$-$\displaystyle 75$ $\displaystyle 9$
Based on the above information, answer the following :(i)Write the median class.(ii)When first ball was picked up, what was the probability of calling out an even number ?(iii)Find median of the given data.Find mode of the given data.
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)
Find median of the given data.
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) $\displaystyle =\frac{37}{75}$
\[\text { (a) } \begin{aligned}
\text { Median } & =30+\frac{\left(\dfrac{48}{2}-17\right)}{10} \times 15 \\
& =40.5
\end{aligned}
\]
(iii)
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 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.