Question

The following Venn diagram model represents the number of students whose favorite colors are either red or blue or both.From the model given above, find the probability of red being the favorite color given that the blue color is also the favorite color.

Answer 1

We should first notice we have a total number of 45 students.

The general formula to calculate conditional probability is

`P(R|B)=(P(R\cap B))/(P(B))`

In this case, as we can see from the diagram,

`P(R\cap B)=(10)/(45)`

and

`P(B)=(35)/(45)+(10)/(45)=(45)/(45)=1`

So using these values in the formula for the conditional probability we get:

`P(R|B)=((10)/(45))/(1)=(10)/(45)`

With this we can see that the correct answer is the first option.