71
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.
OR
(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 = $99$)
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.
OR
(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 = $99$)
Show SolutionHide Solution↓
(i) All possible outcomes: RR, RG, RB, GR, GB, GG, YR, YB, YG
(ii) Number of favourable outcome (RB) $= 1$
$P (\text{Making purple}) = \frac{1}{9}$
(iii)(a) As $P(\text{winning}) = \frac{1}{9}$
Therefore, number of people must win $= \frac{1}{9} \times 99 = 11$
$\therefore$ Game lost by $88$ persons.
Funds collected $= 5 \times 88 - 10 \times 11 = \text{Rs}330$
OR
(iii)(b) Number of participants $= 99$
$P(\text{winning the game}) = \frac{1}{9}$
Number of persons won $= 11$
Number of persons lost $= 88$
Funds collected $= 88 \times 5 - 11 \times 5 = \text{Rs}385$
(ii) Number of favourable outcome (RB) $= 1$
$P (\text{Making purple}) = \frac{1}{9}$
(iii)(a) As $P(\text{winning}) = \frac{1}{9}$
Therefore, number of people must win $= \frac{1}{9} \times 99 = 11$
$\therefore$ Game lost by $88$ persons.
Funds collected $= 5 \times 88 - 10 \times 11 = \text{Rs}330$
OR
(iii)(b) Number of participants $= 99$
$P(\text{winning the game}) = \frac{1}{9}$
Number of persons won $= 11$
Number of persons lost $= 88$
Funds collected $= 88 \times 5 - 11 \times 5 = \text{Rs}385$