Answer:
25% probability you will roll a prime number and spin a prime number
Step-by-step explanation:
If we have two events, A and B, and they are independent, we have that:
![P(A \cap B) = P(A) \times P(B)](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%5Ctimes%20P%28B%29)
In this question:
Event A: Rolling a prime number.
Event B: Spinning a prime number.
Both the cube and the spinner have four values, ranging from one to four.
2 and 3 are prime values, that is, 2 of those values. Then
![P(A) = P(B) = \frac{2}{4} = \frac{1}{2}](https://tex.z-dn.net/?f=P%28A%29%20%3D%20P%28B%29%20%3D%20%5Cfrac%7B2%7D%7B4%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
What is the probability you will roll a prime number and spin a prime number
The cube and the spinner are independent of each other. So
![P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%3D%200.25)
25% probability you will roll a prime number and spin a prime number