Answer to Question #226653 in Statistics and Probability for Courage Chikumbiri

Question

1 Proffessor Ndlovu wishes to choose one child at random from the eleven children in his music class. The children are numbered 2, 3, 4, and so on, up to 12. The Proffessor then throws two fair dice, each numbered from 1 to 6, and chooses the child whose number is the sum of the scores on the two dice.

i. Explain why this is an unsatisfactory method of choosing a child

Answer 1

Two dice are rolled one time

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ \hdashline 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ \hdashline 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ \hdashline 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ \hdashline 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hdashline 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6 \\ \hline \end{array}$$

$$1+1=2, p=1/36$$

$$1+2=2+1=3, p=2/36$$

$$1+3=2+2=3+1=4, p=3/36$$

$$1+4=2+3=3+2=4+1=5, p=4/36$$

$$1+5=2+4=3+3=4+2=5+1=6, p=5/36$$

$$1+6=2+5=3+4=4+3=5+2=6+1=7, p=6/36$$

$$2+6=3+5=4+4=5+3=6+2=8, p=5/36$$

$$3+6=4+5=5+4=6+3=9, p=4/36$$

$$4+6=5+5=6+4=10, p=3/36$$

$$5+6=6+5=11, p=2/36$$

$$6+6=12, p=1/36$$

One or more outcomes are more likely to occur than others and the event would be unfair.

Hence this is an unsatisfactory method of choosing a child.