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A fair tetrahedral die has four triangular faces, numbered 1, 2, 3 and 4. The score when this die is
thrown is the number on the face that the die lands on. This die is thrown three times. The random
variable X is the sum of the three scores.
(i) Show that P(X = 9) = 10/64
(ii) Copy and complete the probability distribution table for X. [3]
(iii) Event R is ‘the sum of the three scores is 9’. Event S is ‘the product of the three scores is 16’.
Determine whether events R and S are independent, showing your working. [5]

It's from W'12 P62 Q6.
 
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