Question

You are experimenting with spinning a fair spinner with 8 numbered spaces and you spin a 1,2,3 or 4 on the first several spins. So, you let x be a random variable that represents the number of 1’s through 4’s that have been spun prior to the first 5 through 8 spins. Draw a histogram of the distribution of P(x) for up to ten spins. If you spin the spinner 3 times and the first 2 spins are 1 through 4, are you more likely to get 5 through 8 on the third spin? Explain.

Answer 1

> count-rep (0,1000) > for (j in 1:1000) + count [j]-o + a-rep (0,10) + b-rep(o,10) + for i in 1:10)0 +bi]-sample(1:8,1) +f (i>1&&aiJ>ai-1) (count [j]-count [j]+1 > barplot (table(count))

Performed the above experiment in R

400 300 200 100

The histogram above shows that there maximum times there were 2 intervals out of 10 where the number of 1’s through 4’s that have been spun prior to the first 5 through 8 spins.

The ans may be different for different systems as this is a randomized example.

As per the law of averaging we can always say that

If you spin the spinner 3 times and the first 2 spins are 1 through 4, are you more likely to get 5 through 8 on the third spin.

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