8. Alwena regularly travels from Anglesey to Cardiff to attend meetings. For each meeting, she chooses one of three ways to travel: by plane, train or car.
The probability of a meeting being held on a Saturday is 0·08.
The probability that Alwena travels by plane to a meeting is 0·15. The probability that she travels by train is 0·45.
Her decision on how to travel is independent of the day on which the meeting is held.
(a) Complete the following tree diagram. [3]
(b) A meeting is chosen at random. Calculate the probability that the meeting is held on a Saturday and that Alwena travels by plane or by car. [3]
Mark scheme (a)
Scheme
Marks
Comments
0·92 written on the ‘Not a Saturday’ branch.
B1
Sight of 1 − 0·15 − 0·45 OR 0·4 or 0·40
B1
Allow this B1 if shown on working lines.
0·4(0) on both ‘car’ branches AND 0·15 AND 0·45 correctly shown on lower branches.
B1
Mark scheme (b)
Scheme
Marks
Comments
Sight of 0·08 × 0·15 OR 0·08 × 0·4 or equivalent.
B1
FT ‘their P(car)’ if <1.
(P(Sat and ‘plane or car’) =) 0·08 × 0·15 + 0·08 × 0·4 or equivalent
M1
0·08 × 0·55 implies previous B1.
= 0·044 or equivalent. ISW
A1
Alternative method
Scheme
Marks
Comments
(P(Sat and ‘plane or car’) =) 1 – (0·92 + 0·08 × 0·45) or equivalent
M2
FT ‘their 0·92’. M1 for intent P(Sat and ‘plane or car’) = 1 – P(‘not Saturday’) – P(‘Saturday and train’)
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