4MA0 Higher January 2017 Paper 4R Q12
12 Joaquim takes part in two cycle races.
The probability that he wins the first race is 0.6
The probability that he wins the second race is 0.7
(a) Complete the probability tree diagram. (2)
(b) Work out the probability that Joaquim wins both races. (2)
Joaquim takes part in a third cycle race.
The probability that Joaquim wins the third race is 0.2
(c) Work out the probability that he wins exactly one of the three races. (3)
| Scheme | Marks |
|---|---|
| Correct probabilities | B1 |
| B1 | |
| (2) |
Notes
B1: For 0.4 on LH branch
B1: For 0.3, 0.7 and 0.3 on RH branches
| Scheme | Marks |
|---|---|
| M1 | |
| 0.42 | A1 |
| (2) |
Notes
M1: For 0.6 × 0.7
A1: oe
| Scheme | Marks |
|---|---|
| 0.6 × “0.3” × “0.8” + “0.4” × 0.7 × “0.8” + “0.4” × “0.3” × 0.2 (= 0.144 + 0.224 + 0.024) oe | M2ft |
| 0.392 | A1cao |
| (3) | |
| (7 marks) |
Notes
M2ft: For a complete method
M1ft for 0.6 × “0.3” × “0.8” or 0.144 \(\left(\dfrac{18}{125}\right)\) or “0.4” × 0.7 × “0.8” or 0.224 \(\left(\dfrac{28}{125}\right)\) or “0.4” × “0.3” × 0.2 or 0.024 \(\left(\dfrac{3}{125}\right)\)
A1cao: \(\dfrac{49}{125}\) oe
Alternative method
| Scheme | Marks |
|---|---|
| 1 – [(0.6 × 0.7 × 0.2) + (0.4 × 0.3 × 0.8) + (0.6 × 0.7 × 0.8) + (0.6 × 0.3 × 0.2) + (0.4 × 0.7 × 0.2)] | M2ft |
| 0.392 | A1cao |
Notes
M2ft: For complete method
M1ft for 1 – (at least 2 correct products).
A1cao: \(\dfrac{49}{125}\)