smc-638-40-Graph

Shown below is the graph of `p`, which is the probability function for the number of times, `x`, that a ' 6 ' is rolled on a fair six-sided die in 20 trials.

Let `q` be the probability function for the number of times, `w`, that a ' 6 ' is not rolled on a fair six-sided die in 20 trials. `q(w)` is given by

`p(20-w)`
`p(1-(w)/( 20))`
`p((w)/( 20))`
`p(w-20)`
`1-p(w)`

Show Answers Only

`A`

Show Worked Solution

`q∼text(Bi)(20,(5)/(6)),quad p∼text(Bi)(20,(1)/(6))`

♦ Mean mark 45%.

`q(19)=([20],[19])((5)/(6))^(19)((1)/(6))=p(1)=([20],[1])((1)/(6))((5)/(6))^(19)`

`q(18)=([20],[18])((5)/(6))^(18)((1)/(6))^(2)=p(2)=([20],[2])((1)/(6))^(2)((5)/(6))^(18)`

`text(Generally,)`

`g(w)=([20],[w])((5)/(6))^(w)((1)/(6))^(20-w)=p(20-w)=([20],[20-w])((1)/(6))^(20-w)((5)/(6))^(w)`

`q(w)=p(20-w)`

`=>A`