A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2018 · Q26 Marks
A fair 6-sided die has the numbers -1, -1, 0, 0, 1, 2 on its faces. A fair 3-sided spinner has edges numbered -1, 0, 1. The die is thrown and the spinner is spun. The number on the uppermost face of the die and the number on the edge on which the spinner comes to rest are noted. The sum of these two numbers is denoted by X.
- (i)Draw up a table showing the probability distribution of X.[3]
- (ii)Find Var(X).[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] -2, -1, 0, 1, 2, 3 seen as top line of a pdf table OR attempting to evaluate P(-2), P(−1), P(0), P(1), P(2), P(3),
- [B1] At least 4 probs correct (need not be in table)
- [B1] All probs correct in a table
- [M1] Correct unsimplified expression for the mean using their table, Σp = 1, may be implied
- [M1] Correct, unsimplified expression for the variance using their table, and their mean2 subtracted. Allow Σp ≠ 1
- [A1] Correct answer (65/36, (1.81))
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