Question

the numbered disks shown are placed in a box and one disk is selected at random. find the probability of selecting a 5, given that a green disk is selected. find the probability of selecting a 5, given that a green disk is selected. (type an integer or a simplified fraction )

Explanation:

Step1: Determine the number of green disks

There are 7 green disks (disks numbered 1, 2, 3, 4, 5, 6, 7).

Step2: Determine the number of green disks with the number 5

There is 1 green disk with the number 5.

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (selecting a 5 among green disks) is 1, and the total number of outcomes (selecting any green disk) is 7. So \(P = \frac{1}{7}\).

Answer:

\(\frac{1}{7}\)