From the sample space sequals={1, 2, 3, 4,..., 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(upper a vertial line upper ba∣b).
Accepted Solution
A:
Given E={1,2,3,4,5....14,15}.... sample space A={2,4,6,...14} ..... even numbers B={4,8,12} ............multiples of 4 To find: P(A|B)
We deduce from above that P(A)=7/15 P(B)=3/15 P(A ∩ B)=3/15 since B is a subset of A.
The conditional probability P(A|B) is the probability of A happening given B has already happened. So if a number has been selected, and it is known that B has happened, (i.e. multiple of 4), we know that there is a 100% probability A has happened (even).
Mathematically, P(A|B) is defined as P(A ∩ B)/P(B). So P(A|B) =P(A ∩ B)/P(B) =(3/15)/(3/15) =1 (as reasoned above).