Question

If given p(a) = 1/4, p(b)=1/3 and p(aub)= 1/2. value of p(a/b) is

Answer 1

p (a/b)=p (anb)/p (b) is equal to 1/4

Answer 2

Answer:

$p(a/b) =\frac{1}{4}$  

Step-by-step explanation:

Given :

$p(a) =\frac{1}{4}$

$p(b) =\frac{1}{3}$

$p(a\cup b) =\frac{1}{2}$

To find: $p(a/b)$

Solution :

Formula : $p(a/b) =\frac{p(a\cap b)}{p(b)}$   --1

Now to find $p(a\cap b)$

we will use another formula :

$p(a \cup b) =p(a)+p(b)-p(a \cap b)$

Substitute the given values

$\frac{1}{2} =\frac{1}{4}+\frac{1}{3}-p(a \cap b)$

$\frac{1}{2} =\frac{7}{12}-p(a \cap b)$

$p(a \cap b)=\frac{7}{12}-\frac{1}{2}$

$p(a \cap b)=\frac{1}{12}$

Now substitute the values in 1

$p(a/b) =\frac{\frac{1}{12}}{\frac{1}{3}}$  

$p(a/b) =\frac{1}{4}$  

Hence the value of  $p(a/b) =\frac{1}{4}$