19 Machine A and machine B make bottles. The probability that a bottle made by machine A is faulty is 0.02 The probability that a bottle made by machine B is faulty is 0.05
(a) Complete the probability tree diagram.(2)
Shazia takes at random one bottle made by machine A and one bottle made by machine B.
(b) Work out the probability that at least one of these bottles is faulty. (3)
Mark scheme (a)
Answer
Mark
Notes
0.98 0.95, 0.05, 0.95
2
B1 for 0.98 oe for machine A B1 for 0.95, 0.05, 0.95 in correct positions for machine B
Mark scheme (b)
Answer
Mark
Notes
0.069
3
M1 for \(0.02 \times 0.05\) or \(0.02 \times \text{``}0.95\text{''}\) or \(\text{``}0.98\text{''} \times \text{``}0.05\text{''}\) or \(\text{``}0.98\text{''} \times \text{``}0.95\text{''}\) M1 for \(0.02 \times 0.05 + 0.02 \times \text{``}0.95\text{''} + \text{``}0.98\text{''} \times \text{``}0.05\text{''}\) or \(1 - \text{``}0.98\text{''} \times \text{``}0.95\text{''}\) A1 for 0.069 oe
