the numbered disks shown are placed in a box and one disk is selected at random. find the probability of…
the numbered disks shown are placed in a box and one disk is selected at random. find the probability of selecting a green disk, given that an even number is selected.\nwhat is the probability of selecting a green disk, given that an even number is selected?\n(type an integer or a simplified fraction.)
Answer
Explanation:
Step1: Determine the number of even - numbered disks
The even - numbered disks are (2), (4), (6), (8). So, (n(\text{even})=4).
Step2: Determine the number of even - numbered green disks
The even - numbered green disk is (4) and (6). So, (n(\text{even and green}) = 2).
Step3: Use the formula for conditional probability
The formula for conditional probability is (P(A|B)=\frac{P(A\cap B)}{P(B)}). In the case of equally - likely outcomes, (P(\text{green}|\text{even})=\frac{n(\text{even and green})}{n(\text{even})}). Substitute (n(\text{even and green}) = 2) and (n(\text{even})=4) into the formula: (P(\text{green}|\text{even})=\frac{2}{4}).
Answer:
(\frac{1}{2})