Question

Sunny has a six-sided number cube labeled with the numbers 1 through 6 and a spinner, shown below. What is the probability that Sunny rolls a number on the number cube that is greater than or equal to 5 and that the spinner lands on a section labeled A

Answer 1

`P(Cube \ge 5\ and\ Spin[A]) = (1)/(24)`

Explanation:

Given

`Cube = \{1,2,3,4,5,6\}`

`n(Cube) = 6`

`Spinner = \{A,B,C,D,E,F,G,H\}`

`n(Spinner) = 8`

See attachment for spinner

Required

`P(Cube \ge 5\ and\ Spin[A])`

On a number cube, we have:

`Cube \ge 5 = \{5,6\}` ---- i.e. 2 outcomes

So, the probability is:

`P(Cube \ge 5) = (n(Cube \ge 5))/(n(Cube))`

`P(Cube \ge 5) = (2)/(6)`

`P(Cube \ge 5) = (1)/(3)`

On the spinner, we have:

`Spin [A] = \{A\}` ---- i.e. 1 outcomes

So, the probability is:

`P(Spin[A]) = (n(Spin[A]))/(n(Spinner))`

`P(Spin[A]) = (1)/(8)`

`P(Cube \ge 5\ and\ Spin[A])` is calculated as thus:

`P(Cube \ge 5\ and\ Spin[A]) = P(Cube \ge 5) * P(Spin[A])`

`P(Cube \ge 5\ and\ Spin[A]) = (1)/(3) * (1)/(8)`

`P(Cube \ge 5\ and\ Spin[A]) = (1)/(24)`