16. Visitors to the top of Snowdon can either walk up the mountain or take the mountain railway from Llanberis. On a particular day, a visitor to the top of Snowdon is chosen at random. The probability that this person is female is 0·42. The probability that this person took the train is 0·35.
The decision to walk or take the train is independent of gender.
(a) Complete the tree diagram shown below. [3]
(b) The person chosen at random receives a gift voucher. What is the probability that this person is female and travelled up the mountain by train? [2]
Mark scheme (a)
Scheme
Marks
Comments
0·58 on ‘Male’ branch.
B1
0·65 and 0·35 correctly shown on both pairs of branches.
B2
B1 if correctly shown on one pair only. SC1 if 0·65 and 0·35 consistently reversed on all branches.
Mark scheme (b)
Scheme
Marks
Comments
0·42 × 0·35
M1
FT ‘their 0·35’ (on ‘uppermost train branch’) provided less than 1
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