15 Ryan shoots an arrow at a target. He then kicks a ball at a goal.
The probability that Ryan hits the target is \(\dfrac{2}{3}\).
The probability that Ryan scores a goal is \(\dfrac{3}{5}\).
(a) Complete the tree diagram.
[2]
(b) Find the probability that Ryan
(i) misses the target and does not score a goal, [2]
(ii) either hits the target or scores a goal or both. [2]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Correct tree diagram
2
B1 for \(\dfrac{1}{3}\) correctly placed on first branch B1 for \(\dfrac{3}{5}\) and \(\dfrac{2}{5}\) correctly placed on both sets of second branches
Accept equivalent fractions and decimals with \(\dfrac{1}{3}\) at least 0.33
Mark scheme (b)
Answer
Marks
Part marks and guidance
(i) \(\dfrac{2}{15}\) oe nfww
2
FTtheir (a) M1 for their \(\dfrac{1}{3}\) × their \(\dfrac{2}{5}\)
FT their fractions < 1 Ignore attempts to cancel or change to decimal or percentage once correct answer seen Do not accept words or ratios Accept 0.13[3...] or 13[.3...]% If no working seen answer must be correct
(ii) \(\dfrac{13}{15}\) oe nfww
2
FTtheir (i) M1 for 1 – their \(\dfrac{2}{15}\)
ALTERNATIVE with each of their fractions < 1 M1 for \(\dfrac{2}{3} \times \dfrac{3}{5} + \dfrac{2}{3} \times \dfrac{2}{5} + \dfrac{1}{3} \times \dfrac{3}{5}\) or \(\dfrac{2}{3} + \dfrac{1}{3} \times \dfrac{3}{5}\)
FT their fractions < 1 Do not accept words or ratios Accept 0.86 to 0.87 or 86% to 87% If no working seen answer must be correct Ignore attempts to cancel or change to decimal or percentage once correct answer seen
May be implied by \(\dfrac{6}{15} + \dfrac{4}{15} + \dfrac{3}{15}\) or \(\dfrac{2}{3} + \dfrac{3}{15}\)
