Question

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

Explanation:

Step1: Count green disks

There are 7 green disks.

Step2: Count green - odd - numbered disks

The odd - numbered green disks are 1, 3, 5, 7, so there are 4 green - odd - numbered disks.

Step3: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of equally - likely outcomes, if $A$ is the event of selecting an odd number and $B$ is the event of selecting a green disk, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$. So the probability is $\frac{4}{7}$.

Answer:

$\frac{4}{7}$