17. Dylan is having a weekend break in Wrexham. The probability that he will visit Erddig Gardens is 0·7. The probability of Dylan going to the Bersham Heritage Centre is independent of him visiting Erddig Gardens.
The probability that he visits Erddig Gardensand goes to the Bersham Heritage Centre is 0·28.
(a) Complete the following tree diagram. [4]
(b) Calculate the probability that Dylan visits Erddig Gardens but does not go to the Bersham Heritage Centre. [2]
Mark scheme (a)
Scheme
Marks
Comments
0·3 shown for ‘Does not visit ‘Erddig Gardens’.
B1
Use of 0·7 × …… = 0·28
M1
Implied by sight of 0·4 (on ‘top branch’ of the four on the right.)
P(goes to ‘Bersham Heritage Centre’) = 0.4
A1
Second set of branches 0·4, 0·6, 0·4, 0·6
A1
FT ‘their 0·4’ BUT dependent on M1 gained. (i.e. M0A0A0 for 0·28 and 0·72 on branches.)
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