15. Evan and Jane each shoot one arrow at a target. The probability that Evan hits the centre of the target is 0·4. The probability that Jane hits the centre of the target is 0·45.
(a) Complete the tree diagram below. [3]
(b) Find the probability that Evan and Jane both hit the centre of the target. [2]
Mark scheme (a)
Scheme
Marks
Comments
0·6 or equivalent on correct Evan branch.
B1
0·45 and 0·55 or equivalent correctly shown on both pairs for Jane.
B2
Award B1 for one of the following:
0·45 and 0·55 or equivalent correctly shown on one pair of Jane’s branches only
0·45 and 0·55 or equivalent consistently reversed on all Jane branches.
Notes
The answers on the tree diagram were printed in red in the original; they are shown in black here.
Mark scheme (b)
Scheme
Marks
Comments
0·4 × 0·45 or equivalent
M1
FT 0·4 × ‘Jane’s probability of hitting the centre’ provided less than 1.
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