Question

A middle school decided to run the following spinner game as a fundraiser on Christmas Carnival. Making purple: Spin each spinner once. Blue and red makes 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 information, answer the following questions.

1. List all possible outcomes of the game.
2. Find the probability of ‘making purple’.
3. For each win, a participant gets ₹ 10, but if he/she loses, he/she has to pay ₹ 5 to the school. If 99 participants played, calculate how much fund the school could have collected.
4. If the same amount of ₹ 5 has been decided for winning or losing the game then how much fund had been collected by the school? (Number of participants (= 99).

Answer 1

Given Data:

Spinner 1 options: Red (R), Green (G), Yellow (Y)

Spinner 2 options: Red (R), Green (G), Blue (B)

i. All possible outcomes of the game:

Combining the outcome of spinner 1 followed by spinner 2: \[\text{Sample Space } (S) = {RR, RG, RB, GR, GG, GB, YR, YG, YB}\]

Total number of outcomes: n(S) = 9

ii. Probability of ‘making purple’:

Purple is formed only by the combination of Red and Blue.

Since only Spinner 1 has Red and Spinner 2 has Blue, the only winning outcome is RB.

Number of favourable outcomes: n(E) = 1

Formula and Calculation: \[P(\text{making purple}) = \frac{n(E)}{n(S)} = \frac{1}{9}\]

iii. Fund collected with ₹ 10 win payout and ₹ 5 loss collection (for 99 participants):

Expected number of winners: \[\text{Winners} = 99 \times P(\text{making purple}) = 99 \times \frac{1}{9} = 11\]

Number of losers: \[\text{Losers} = 99 - 11 = 88\]

Financial Breakdown:

Amount collected from losers: \[88\ \times ₹,5 = ₹,440\]

Amount given to winners: \[11\ \times ₹,10 = ₹,110\]

Net fund collected by the school: \[₹,(440 - 110) = ₹,330\]

iv. Fund collected with ₹ 5 for winning or losing (for 99 participants):

Winners get ₹ 5 each, losers pay ₹ 5 each.

Net fund collected: \[(88\ \times ₹,5) - (11\ \times ₹,5) = ₹,(440 - 55) = ₹,385\]