14 A target has a black circle and a white region. Arrows can hit the black circle, the white region or miss the target.
Peter shoots two arrows at the target. On each shot, the probability that Peter’s arrow misses the target is 0.1 On each shot, the probability that Peter’s arrow hits the white region is twice the probability that it hits the black circle.
(a) Complete the probability tree diagram for Peter’s two arrows.(3)
(b) An arrow which hits the black circle scores 10 points. An arrow which hits the white region scores 5 points. An arrow which misses the target scores 0 points.Calculate the probability that Peter scores exactly 10 points with his 2 arrows. (3)
Mark scheme (a)
Scheme
Marks
Black circle = 0.3 White region = 0.6
B1 B1
All values “correct” for second shot
B1ft
(3)
Notes
B1ft: Allow ft if each group of 3 branches on second arrow all sum to 1 and are consistent with first arrow branches
Mark scheme (b)
Scheme
Marks
Any one correct product in numerical form e.g. (“0.3” x 0.1) or (0.1 x “0.3”) or (“0.6” x “0.6”)
M1ft
(“0.3” x 0.1) + (0.1x “0.3”) + (“0.6” x “0.6”)
M1ft
0.42oe
A1
(3)
Notes
M1ft: e.g. (Black, Miss) or (Miss, Black) or (White, White)
