The probability that Freya will pass the exam is 0.8 The probability that Ria will pass the exam is 0.85
(a) Complete the probability tree diagram.(2)
(b) Work out the probability that only one of Freya or Ria will pass the exam. (3)
Mark scheme (a)
Answer
Mark
Mark scheme
0.2, 0.15, 0.85, 0.15
B2
all placed correctly
(B1
for 2 or 3 placed correctly)
Mark scheme (b)
Answer
Mark
Mark scheme
0.29
M1
for one correct product, ft their tree diagram eg \(0.8 \times 0.85\ (= 0.68)\) or \(0.8 \times \text{``}0.15\text{''}\ (= 0.12)\) or \(\text{``}0.2\text{''} \times \text{``}0.85\text{''}\ (= 0.17)\) or \(\text{``}0.2\text{''} \times \text{``}0.15\text{''}\ (= 0.03)\)
M1
for a complete method, ft their tree diagram eg \(\text{``}0.2\text{''} \times \text{``}0.85\text{''} + 0.8 \times \text{``}0.15\text{''}\) or \(1 - (0.8 \times 0.85 + \text{``}0.2\text{''} \times \text{``}0.15\text{''})\)
A1
for 0.29 oe or ft their tree diagram
Additional guidance
Working for part (b) may be seen in part (a) To apply ft values must be <1
