Probability Distributions - A Level Math

1. Two fair dice are thrown. If the scores are unequal, the larger of the two scores is recorded. If the scores are equal then that score is recorded. Let X denote the number recorded.

a) show that P(X = 2) = 1/12 and draw up a table showing the probability distribution of X

Ans:

Two fair dice {6 sided}

Scores - unequal:

1. 1+1=1 {X =1}
2. 2+1=3 {X = 2}
3. 1+2=3 {X = 2}
4. 2+2=4 {X = 2]
5. 2+2=4 {X = 2}
6. 2+3=5 {X = 3}
7. 3+2=5 {X = 3}
8. 3+3=6 {X = 3}
9. 3+3=6 {X = 3}
10. 3+4=7  {X = 4}
11. {X = 4}
12. {X = 4}
13. {X = 4}
14. {X = 5}
15. {X = 5}
16. {X = 5}
17. {X = 5}
18. {X = 6}
19. {X = 6}
20. {X = 6}
21. {X = 6}

etcetera...

P(X=2)

 X=2 == 4/21 if 1/12 then {1.9/21} e.g. 

Calculation Based On: 2/21 (Equal)
0.95/21 = 0.045[recurring]

Calculation Based On: 2/21 (Unequal)

0.95/21 = 0.045[recurring]

Thank you.

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