O-LevelMathematicsProbability4024/22 · Oct/Nov 2014 · Q39 Marks

[Figure 3.1] In a game, when it is Mary's turn, she spins each of these fair spinners once. Mary's score for the turn is worked out using the formula xm + yn, where x is the number on spinner X and y is the number on spinner Y. The possibility space diagram shows Mary's possible scores. [Table 3.1] x (number on spinner X) y (number on spinner Y) -4 | 37 | 47 | 67 | 97 -1 | 28 | 38 | 58 | 88 3 | 16 | 26 | 46 | 76 4 | 13 | 23 | 43 | 73

(a)Find the probability that Mary's score is less than 15.[1]
(b)Calculate the probability that on two consecutive turns, Mary scores less than 40 on one and more than 75 on the other.[3]
(c)(i)The diagram shows 7 on spinner X and –1 on spinner Y. Using the formula, the score for this turn is 7m – n = 38. Using the table, find 7m + 3n.[1]
(c)(ii)Hence find m and n.[2]
(d)Find p.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

[1] 1/16 or 0.0625
[3] 42/256 or 0.164 oe
[3] B2 for (2)× 7/16 × 3/16 or B1 for both 7/16 and 3/16 or SC1 after 0 for 7/40
[1] 26
[2] m = 5 n = −3
[2] B1 for one correct or M1 for correct substitution and evaluation of the other variable or for an equation in one variable
[2] p = 17
[2] M1 for p× theirm – 4× theirn(= 97) oe

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