Q) 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 10, but if he/she loses,
he/she has to pay 5 to the school. If 99 participants played, calculate how much fund could the school have collected.
(iii) (b) If the same amount of 5 has been decided for winning or losing the game, then how much fund had been collected by school? (Number of participants = 99)
(i) All possible outcomes of the game:
Since each color on 1st spinner can combine with each of the 3 colors on 2nd spinner.
Therefore, possible combinations by Red color: RR, RB, RG
Possible combinations by Green color: GR, GB, GG
Possible combinations by Yellow color: YR, YB, YG
Hence, total combinations = 3 x 3 = 9
(ii) probability of making purple:
Since, it is given that purple color is made by combinations of RB, there is 1 such combination.
The probability of making purple =
(iii)(a) Fund collected at Rs. 10 as winning amount:
Since the probability of winning (i.e. making purple) =
Hence, number of participants who won the game = 99 x = 11
Participants who lost the game = 99 – 11 = 88
Therefore, the fund collected =
5 x 88 – 10 x 11 = Rs. 330
(iii)(b) Fund collected at Rs. 5 as winning amount:
If winning amount is also 5, then fund collected =
5 x 88 – 5 x 11 = Rs. 385