8. Beti walks her dog to a local park and back home every day. She can either walk along a footpath or along a pavement at the side of a road.
The probability that Beti walks to the park along the footpath is \(\dfrac{3}{5}\).
The probability that Beti walks home from the park along the road is \(\dfrac{2}{7}\).
Her decisions on which routes to walk to and from the park are independent of each other.
(a) Complete the tree diagram below. [2]
(b) Find the probability that Beti walks to and from the park along the footpath. [2]
Mark scheme (a)
Scheme
Marks
Comments
Complete diagram
B2
If B2 not awarded, award B1 for one of the following:
2/5 or equivalent on Road to the park branch
5/7 on a Footpath from the park branch.
Mark scheme (b)
Scheme
Marks
Comments
\(\dfrac{3}{5} \times \dfrac{5}{7}\) or equivalent
M1
FT \(\dfrac{3}{5}\) × ‘their \(\dfrac{5}{7}\)’ (on ‘uppermost footpath home branch’) provided less than 1.
\(\dfrac{15}{35}\) or equivalent ISW
A1
Corrected by Westie's Workshop
The board's mark scheme printed “FT \(\dfrac{3}{7}\) × ‘their \(\dfrac{5}{7}\)’”. Changed to “FT \(\dfrac{3}{5}\) × ‘their \(\dfrac{5}{7}\)’” because the probability of walking to the park along the footpath is \(\dfrac{3}{5}\), and only the second fraction (‘their \(\dfrac{5}{7}\)’) can be followed through.
Original: see the board's mark scheme PDF (link above).
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