4MA0 Higher June 2012 Paper 3 Q10
10 The table shows information about the number of peas in each of 25 pods.
| Number of peas | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Number of pods | 3 | 6 | 5 | 8 | 2 | 1 |
He takes at random one of the pods.
Find the probability that he takes a pod with 3 peas or a pod with 4 peas. (2)
She takes at random two pods without replacement.
Calculate the probability that
| Scheme | Marks |
|---|---|
| 1×3 + 2×6 + 3×5 + 4×8 + 5×2 + 6×1 or 3 + 12 + 15 + 32 + 10 + 6 or 78 | M1 |
| “78” ÷ 25 | M1 |
| 3.12 oe inc \(3\frac{3}{25}\), \(\frac{78}{25}\) | A1 |
| (3) |
Notes
M1: for finding at least 4 correct products and summing them
M1: (dep) for division by 25
Accept division by their 25, if addition shown.
A1: Also accept 3 or 3.1 if both method marks scored
Apart from Questions 9, 13, 18, 20 and 21 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| 5 + 8 or 13 or \(\frac{5}{25} + \frac{8}{25}\) | M1 |
| \(\frac{13}{25}\) oe | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| (i) \(\frac{5}{25} \times \frac{4}{24}\) oe | M1 |
| \(\frac{20}{600}\) oe | A1 |
| (ii) \(\frac{3}{25} \times \frac{5}{24} + \frac{6}{25} \times \frac{5}{24} + \frac{5}{25} \times \frac{3}{24}\) or \(2 \times \frac{3}{25} \times \frac{5}{24} + \frac{6}{25} \times \frac{5}{24}\) | M1 |
| M1 | |
| \(\frac{60}{600}\) oe | A1 |
| (5) | |
| (Total 10 marks) |
Notes
M1: for \(\frac{5}{25} \times \frac{4}{24}\) oe
A1: for \(\frac{20}{600}\) oe inc \(\frac{1}{30}\)
M1: for one correct product
M1: for sum of all 3 correct products
A1: for \(\frac{60}{600}\) oe inc \(\frac{1}{10}\)
Note for (c)(ii): sample space method – award 3 marks for correct answer; otherwise no marks.
SC M1 for \(\frac{3}{25} \times \frac{5}{25}\) or \(\frac{6}{25} \times \frac{6}{25}\) or \(\frac{5}{25} \times \frac{3}{25}\)
M1 for \(\frac{3}{25} \times \frac{5}{25} + \frac{6}{25} \times \frac{6}{25} + \frac{5}{25} \times \frac{3}{25}\)
or \(2 \times \frac{3}{25} \times \frac{5}{25} + \frac{6}{25} \times \frac{6}{25}\)
SC Sample space method – award 2 marks for \(\frac{66}{625}\); otherwise no marks.