16. Alwyn often drives from Bangor to Cardiff. He always chooses one of two routes for these journeys. He either travels through Rhayader or through Hereford. The probability that he travels through Rhayader is 0·7.
Sometimes he decides to stop for a break during his journey. His decision is independent of the route he takes.
The probability that he travels through Rhayader and stops for a break is 0·42.
(a) Complete the following tree diagram. [4]
(b) Calculate the probability that Alwyn travels through Hereford but does not stop for a break. [2]
Mark scheme (a)
Scheme
Marks
Comments
Ribbon marking for 16(a) and 16(b). 0·3 on ‘Hereford’ branch.
B1
0·7 × P(Yes) = 0·42
M1
Allow their notation for P(Yes).
P(Yes) = 0·6
A1
0·6, 0·4, 0·6 and 0·4 correctly placed.
A1
F.T. ‘their P(Yes)’, if between 0 and 1 but not 0·5.
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