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

Answer:

$P(Cube \ge 5\ and\ Spin[A]) = \frac{1}{24}$

Step-by-step 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:

$P(Cube \ge 5) = \frac{n(Cube \ge 5)}{n(Cube)}$

$P(Cube \ge 5) = \frac{2}{6}$

$P(Cube \ge 5) = \frac{1}{3}$

On the spinner, we have:

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

So, the probability is:

$P(Spin[A]) = \frac{n(Spin[A])}{n(Spinner)}$

$P(Spin[A]) = \frac{1}{8}$

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

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

$P(Cube \ge 5\ and\ Spin[A]) = \frac{1}{3} * \frac{1}{8}$

$P(Cube \ge 5\ and\ Spin[A]) = \frac{1}{24}$