Question

From the sample space S= (1,2,3,4,5,6,6,7,8,9,10,11,12,13,14,15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(A\B).

Answer 1

100%

Explanation:

The first thing is to extract the sample spaces of the events, just like this:

A (even number) = {2, 4, 6, 8, 10, 12, 14}

B (multiple of 4) = {4, 8, 12}

A n B = {4, 8, 12}

Now, we calculate the probability of each case

`\begin{gathered} P(A)=(7)/(15) \\ P(B)=(3)/(15)=(1)/(3) \\ P(A\cap B)=(3)/(15)=(1)/(3) \end{gathered}`

We have that the probability P (A | B) is calculated as follows:

`\begin{gathered} P(A|B)=(P(A\cap B))/(P(B)) \\ \text{ replacing} \\ P(A|B)=((1)/(3))/((1)/(3))=1=100\text{\%} \end{gathered}`

The probability is 100% since every multiple of 4 is even.