22 On a bus route there is a set of traffic lights and a level crossing. The probability that the bus stops at the traffic lights is 0.7. The probability that the bus stops at the level crossing is 0.2.
(a) Use the information to complete the tree diagram.
[3]
(b) Find the probability that the bus stops at either the traffic lights or at the level crossing but not both. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
0.3
1
Accept fractions or percentages
0.2, 0.8, 0.2, 0.8 or 0.2, 0.8, 0.8, 0.2
1
Does not stop, stops, does not stop
1
Diagram must be fully correct for 3 marks
Mark scheme (b)
Answer
Marks
Part marks and guidance
0.62
3
M2 for \(0.7 \times 0.8 + 0.3 \times 0.2\) or better or for \(1 - (0.7 \times 0.2 + 0.3 \times 0.8)\) or better or M1 for one correct product shown or implied
FT for M1 and M2 and 3their 0.8, 0.2 and their 0.3 (must be less than 1)
eg \(0.7 \times 0.8\) or \(0.3 \times 0.2\) or \(0.7 \times 0.2\) or \(0.3 \times 0.8\) soi by 0.56, 0.06, 0.14 or 0.24
