Question

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 the number selected is at least 6. what is the probability of selecting a green disk, given that the number selected is at least 6? (type an integer or a simplified fraction )

Explanation:

Step1: Determine total disks with number at least 6

The disks with number at least 6 are 6, 7, 8. There are 3 such disks.

Step2: Determine green disks among those with number at least 6

The green disk among 6, 7, 8 is the disk numbered 6. There is 1 green disk in this subset.

Step3: Calculate conditional - probability

The formula for conditional probability \(P(A|B)=\frac{n(A\cap B)}{n(B)}\), where \(A\) is the event of selecting a green disk and \(B\) is the event of selecting a disk with number at least 6. Here, \(n(A\cap B) = 1\) (the green disk numbered 6) and \(n(B)=3\). So the probability is \(\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)