A-LevelMathematicsProbability and statistics9709/62 · May/June 2017 · Q46 Marks
Two identical biased triangular spinners with sides marked 1, 2 and 3 are spun. For each spinner, the probabilities of landing on the sides marked 1, 2 and 3 are p, q and r respectively. The score is the sum of the numbers on the sides on which the spinners land. You are given that P(score is 6) = 36 and P(score is 5) = 4. Find the values of p, q and r.
- Two identical biased triangular spinners with sides marked 1, 2 and 3 are spun. For each spinner, the probabilities of landing on the sides marked 1, 2 and 3 are p, q and r respectively. The score is the sum of the numbers on the sides on which the spinners land. You are given that P(score is 6) = 36 and P(score is 5) = 4. Find the values of p, q and r.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- M1 Realising that score 6 is only P(3, 3)
- A1 Correct ans [SR B2 r = 1/6 without workings]
- M1 Eqn involving qr (OE) equated to 1/9 (r may be replaced by their 'r value')
- M1 Correct equation with their 'r value' substituted
- A1 Correct answer seen, does not imply previous M's
- B1 FT FT their p + their r + their q =1, 0<p<1
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