|
Prize Fishing
Forty identical metal fish are put in a bowl. On each fish
there is a coloured spot hidden from view. The different colours
represent prizes of different amounts. Competitors pay to catch a
fish with a magnet. Once a prize is given the fish is put back
before the next person's turn. Every competitor wins a prize.
How Much Should We Charge?
Table 2 shows how much the different colours are worth and how
many fish are marked with each colour.
| Colour |
Prize value |
No. of fish |
Prize value x
No. of fish |
| Blue |
2p |
20 |
40p |
| Green |
3p |
10 |
|
| Yellow |
5p |
5 |
|
| Orange |
10p |
4 |
|
| Red |
25p |
1 |
|
| |
|
Total Value |
|
Table 2 - Prize value of fish in the bowl.
There are 20 blue fish, each with a prize value of 2p. They
are worth 40p altogether.
| a |
How many orange fish are there
in the bowl? |
| b |
What is the prize value of the
orange fish altogether? |
| c |
Copy and complete Table 4 on
page Rl. |
| d |
What is the total prize value of
all the fish in the bowl? |
In a very large number of turns we expect each fish to be
caught the same number of times.
This means on average each fish is caught once in 40 turns.
In every 40 turns we expect to pay about œ1.60.
| e |
What is the average amount paid
out each turn? |
| f |
What would you charge for each
turn? |
| g |
With this charge, what is the
average profit to the school fair for each turn? |
Who Wins?
During the afternoon we expect 800 players. The charge for
each turn is 5p.
| a |
How much profit does the school
fair make on average in one turn with a charge of 5p? |
| b |
How much profit do you expect
this stall to make in the afternoon? |
| c |
What fraction of the fish are
worth less than 5p? |
| d |
What fraction of the players do
you expect to win less than 5p? |
| e |
What is the probability that a
player loses money when playing the game once? |
| f |
What is the probability of
winning the 25p prize? |
A Bigger Prize
Jane says 'Make the red fish worth a prize of 75p. That will
make more people want to play.'The charge is kept at 5p.
| a |
Is Jane right? |
| b |
What is the total value of fish
in the bowl now? |
| c |
What is the average payout per
turn now? |
| d |
Will the school make a bigger
profit if we make this change? |
*More Fish
Gary says 'Leave the prize values as they are. We would make a
lot more profit if we put in 40 black fish and gave no prize for
them.'
| a |
What is the average payout per
turn now? |
| b |
The charge is kept at 5p. What
is the average profit to the school fair for each turn? |
| c |
Is Gary right in what he says?
Give a reason for your answer. |
| 
