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(i) Show that P(X = 9) = i~· [3]
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6 A fair tetrahedral die has four triangular faces, numbered I, 2, 3 and 4. The score when tbis die isthrown is the number on the face that the die lands on. This die is thrown three times. The randomvariable X is the sum of the three scores.
(ii) Copy and complete the probability distribution table for X.
.r 3 4 5 6 7 8 9 10 II 12
P(X = x) 1 3 126-1 6-1 6-1
(iii) Event R is 'the sum of the three scores i 9'. Event S is 'the product of the three scores is 16'.no. . vh ther even Rand S are independent, hewing your working. [5]