4MA0 Foundation June 2012 Paper 1 Q9
9 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 |
(a) Find the mode of the number of peas. (1)
(b) Work out the range of the number of peas. (2)
(c) Work out the mean number of peas in the 25 pods. (3)
(d) Tariq puts the 25 pods in a bag.
He takes at random one of the pods.
Find the probability that he takes
He takes at random one of the pods.
Find the probability that he takes
(i) a pod with 7 peas,
(ii) a pod with 5 peas,
(iii) a pod with 3 peas or a pod with 4 peas.
(5)| Scheme | Marks |
|---|---|
| 4 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| 5 | B2 |
| (2) |
Notes
B2: B1 for 1-6 1 to 6 1,6 etc
| 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 \(3\dfrac{3}{25}\), \(\dfrac{78}{25}\) | 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
| Scheme | Marks |
|---|---|
| (i) Answer: 0 | B1 |
(ii) Answer: \(\dfrac{2}{25}\) | M1 A1 |
| (iii) 5 + 8 or 13 or \(\dfrac{5}{25} + \dfrac{8}{25}\) | M1 |
| \(\dfrac{13}{25}\) | A1 |
| (5) | |
| (Total 11 marks) |
Notes
B1: Also accept \(\dfrac{0}{1}\) or \(\dfrac{0}{25}\)
M1
A1: denominator of 25
numerator of 2