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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 5 · Set 1 · Q37
A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple: Spin each spinner once. Blue and red…
A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival.
Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'. Based on the above, answer the following questions :
(i)
List all possible outcomes of the game.
(ii)
Find the probability of 'Making Purple'.
(iii)
(a)
For each win, a participant gets ₹ $\displaystyle 10$, but if he/she loses, he/she has to pay ₹ $\displaystyle 5$ to the school. If $\displaystyle 99$ participants played, calculate how much fund could the school have collected.
OR
(b)
If the same amount of ₹ $\displaystyle 5$ has been decided for winning or losing the game, then how much fund had been collected by school ? (Number of participants = $\displaystyle 99$)
Marking-scheme solution
(i) All possible outcomes: RR, RG, RB, GR, GB, GG, YR, YB, YG
(ii) Number of favourable outcome (RB) = $\displaystyle 1$
\(\displaystyle P(\) Making purple \(\displaystyle )=\frac{1}{9}\)
(iii)
As \(\displaystyle \mathbf{P}\) (winning) \(\displaystyle =\frac{1}{9}\)
Therefore, number of people must win \(\displaystyle =\frac{1}{9} \times 99=11\)
∴ Game lost by $\displaystyle 88$ persons.
Funds collected \(\displaystyle \boldsymbol{=} \mathbf{5} \boldsymbol{\times} \mathbf{8 8} \boldsymbol{-} \mathbf{1 0} \boldsymbol{\times} \mathbf{1 1} \boldsymbol{=} \mathbf{₹} \mathbf{3 3 0}\)
Number of participants \(\displaystyle \boldsymbol{=} \mathbf{9 9}\)
\(\displaystyle P(\) winning the game \(\displaystyle )=\frac{1}{9}\)
Number of persons won = $\displaystyle 11$
Number of persons lost = $\displaystyle 88$
Funds collected \(\displaystyle =\mathbf{8 8} \times \mathbf{5}-\mathbf{1 1} \times \mathbf{5}=\mathbf{₹} \mathbf{3 8 5}\)
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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.