face numbered 3, two faces numbered 5 and two faces numbered 6. (i) Find the probability of obtaining at least 7 odd numbers in 8 throws of the die. The die is thrown twice. Let X be the sum of the two scores. The following table shows the possible values of X.

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A fair die has one face numbered 1, one face numbered 3, two faces numbered 5 and two faces numbered 6.

(i) Find the probability of obtaining at least 7 odd numbers in 8 throws of the die.

The die is thrown twice. Let X be the sum of the two scores. The following table shows the possible values of X.

                                                                                SECOND THROW

  1 3 5 5 6 6
1 2 4 6 6 7 7
3 4 6 8 8 9 9
5 6 8 10 10 11 11
5 6 8 10 10 11 11
6 7 9 11 11 12 12
6 7 9 11 11 12 12
             

 

(ii) Draw up a table showing the probability distribution of X.(iii) Calculate E(X ).(iv) Find the probability that X is greater than E(X ).

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