20 Reece travels to school by either walking, cycling or using a bus. The probability that Reece walks is always 0.4. The probability that Reece cycles is always 0.55.
(a) Complete the tree diagram for Monday and Tuesday.
[3]
(b) Show that the probability that Reece travels to school by the same method on Monday and Tuesday is 0.465. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
All branches completed with 0.55 and 0.05 in correct places
3
B1 for 0.55 correctly placed at least once B1 for 0.05 correctly placed at least once
M2 for \(0.4 \times 0.4\), \(0.55 \times 0.55\) and \(0.05 \times 0.05\) may be 0.16, 0.3025, 0.0025 or M1 for \(0.4 \times 0.4\) or \(0.55 \times 0.55\) or \(0.05 \times 0.05\) may be 0.16, 0.3025, 0.0025
Answer given: for 3 marks products and additions must be explicitly seen Accept e.g. \((0.4)^2\) for \(0.4 \times 0.4\) Values may be seen on diagram in (a) If all values shown on ends of tree, must select 3 values to use for M2 and 1 value for M1 Equivalent fractions are OK but, for 3 marks must convert to the decimal
