Foundation November 2021 Paper 1 Q15
15 There are 54 fish in a tank.
Some of the fish are white and the rest of the fish are red.
Jeevan takes at random a fish from the tank.
The probability that he takes a white fish is \(\dfrac{4}{9}\)
(a) Work out the number of white fish originally in the tank. (2)
Jeevan puts the fish he took out, back into the tank.
He puts some more white fish into the tank.
Jeevan takes at random a fish from the tank.
The probability that he takes a white fish is now \(\dfrac{1}{2}\)
(b) Work out the number of white fish Jeevan put into the tank. (2)
| Scheme | Marks |
|---|---|
| \(54 \div 9 \times 4\) oe or \(\dfrac{4}{9} \times 54\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 24 | A1 |
| (2) |
Notes
M1: Allow \(0.44(44\ldots) \times 54\) or \(\dfrac{24}{54}\)
| Scheme | Marks |
|---|---|
\(\dfrac{\text{``}{24}\text{''} + n}{54 + n} = \dfrac{1}{2}\) or \(\dfrac{30}{60}\) or 54 – “24” (= 30) and “30” – “24” or 2 × “30” – 54 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 6 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: ft if “24” < 27 or \(\dfrac{6}{60}\)