4MA0 Higher January 2013 Paper 4 Q20
20
In Box X, there are 4 black discs and 1 white disc.
In Box Y, there are 2 black discs and 2 white discs.
Vikram takes at random a disc from Box X and puts it in Box Y.
He then takes at random a disc from Box Y.
(a) Calculate the probability that the disc he takes from Box X and the disc he takes from Box Y will both be black discs. (2)
(b) Calculate the probability that the disc he takes from Box Y will be a white disc. (3)
| Scheme | Marks |
|---|---|
| \(\tfrac{4}{5} \times \tfrac{3}{5}\) | M1 |
| \(\tfrac{12}{25}\) oe | A1 |
| (2) |
Notes
M1: or probability of \(\tfrac{3}{5}\) clearly associated with box Y (eg may be on tree diagram or by box)
| Scheme | Marks |
|---|---|
| \(\tfrac{4}{5} \times \tfrac{2}{5}\), \(\tfrac{1}{5} \times \tfrac{3}{5}\) or 0.32 oe or 0.12 oe | M1 |
| \(\tfrac{4}{5} \times \tfrac{2}{5} + \tfrac{1}{5} \times \tfrac{3}{5}\) | M1 |
| \(\tfrac{11}{25}\) oe | A1 |
| (3) |
Notes
M1: for \(\tfrac{4}{5} \times \tfrac{2}{5}\) or \(\tfrac{1}{5} \times \tfrac{3}{5}\)
M1: for sum of both products