✓ Board-verified↻ asked 3×
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 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)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.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 = $\displaystyle 99$)
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)
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.
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 \(\displaystyle =\mathbf{8 8} \times \mathbf{5}-\mathbf{1 1} \times \mathbf{5}=\mathbf{₹} \mathbf{3 8 5}\)
More from Probability
- The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a…2025 · asked 3×
- Assertion: In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability…2024 · asked 3×
- A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn…2024 · asked 3×
- Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each…2025 · asked 3×
- If a fair coin is tossed twice, find the probability of getting 'atmost one head'.2023 · asked 3×
- A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three…2026 · asked 3×
- Assertion: If probability of happening of an event is 0.2 p, p 0, then p can't be more than 5. Reason (R): P(…2026 · asked 3×
- A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets…2023 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.