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(i) Show that P(X = 9) = i~· [3]

[3]

3 1 \ )

~ • \ 2- '2- , 2- \

3 3 35

t l 2.. 1.. 1- \ 2 \2-

6 L.\ L) 1...,L2'L

r 2. 3 g 2 2. 3 \ :1. \ 3 3)'). 3. 2..\

{ J,. 1.1 '1 L J. \ L-\ .l L\ L\ \ 2 42-1

3 3 ~ \ ~ 33\

.1 :J. 3 :J.. 3 '2. ~ 22

2, 2- ~ ;Z~'L Y 2.2-

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~'Y3

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l-

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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]