4MA0 Higher January 2014 Paper 3 Q13
13 A box contains 20 nails.
The table shows information about the length of each nail.
| Length of nail (mm) | 25 | 30 | 40 | 50 | 60 |
|---|---|---|---|---|---|
| Number of nails | 1 | 8 | 4 | 5 | 2 |
(a) Viraj takes at random one nail from the box.
Find the probability that the length of the nail he takes is
Find the probability that the length of the nail he takes is
(i) 50 mm or 60 mm,
(ii) less than 35 mm.
(4)(b) Jamila puts all 20 nails into a bag.
She takes at random one of the nails and records its length.
She replaces the nail in the bag.
She then takes at random a second nail from the bag and records its length.
Calculate the probability that the two nails she takes
She takes at random one of the nails and records its length.
She replaces the nail in the bag.
She then takes at random a second nail from the bag and records its length.
Calculate the probability that the two nails she takes
(i) each have a length of 60 mm,
(ii) have a total length of 80 mm.
(5)| Scheme | Marks |
|---|---|
| (i) 5 + 2 or 7 or \(\frac{5}{20} + \frac{2}{20}\) | M1 |
| \(\frac{7}{20}\) oe | A1 |
| (ii) | M1 |
| \(\frac{9}{20}\) oe | A1 |
| (4) |
Notes
A1: accept answer written as an equivalent fraction or 0.35 or 35%
M1: for \(\dfrac{9}{a}\) with \(a \gt 9\) or \(\dfrac{b}{20}\) with \(b \lt 20\)
or 9 and 20 used with incorrect notation (eg. 9 : 20)
A1: accept answer written as an equivalent fraction or 0.45 or 45%
| Scheme | Marks |
|---|---|
| (i) \(\frac{2}{20} \times \frac{2}{20}\) oe and no other terms | M1 |
| \(\frac{4}{400}\) oe | A1 |
| (ii) \(\frac{5}{20} \times \frac{8}{20}\) or \(\frac{8}{20} \times \frac{5}{20}\) or \(\frac{4}{20} \times \frac{4}{20}\) | M1 |
| \(\frac{5}{20} \times \frac{8}{20} + \frac{8}{20} \times \frac{5}{20} + \frac{4}{20} \times \frac{4}{20}\) | M1 |
| \(\frac{96}{400}\) oe | A1 |
| (5) | |
| (9 marks) |
Notes
M1: SC M1 for \(\dfrac{2}{20} \times \dfrac{1}{19}\)
A1: accept answer written as an equivalent fraction eg \(\frac{1}{100}\) or 0.01 or 1%
M1: SC M1 for \(\frac{5}{20} \times \frac{8}{19}\) or \(\frac{8}{20} \times \frac{5}{19}\) or \(\frac{4}{20} \times \frac{3}{19}\)
M1: M1 for \(\frac{5}{20} \times \frac{8}{19} + \frac{8}{20} \times \frac{5}{19} + \frac{4}{20} \times \frac{3}{19}\)
A1: accept answer written as an equivalent fraction eg \(\frac{6}{25}\) or 0.24 or 24%