Question

P(A) = 1/3, p(B)= 1/5 and P (A U B) = 11/30
then find P (A/B).​

Answer 1

Answer:

$\sf\\ \\\implies P \left(\dfrac{A}{B}\right) = \left (\dfrac{\dfrac{1}{12}}{\dfrac{1}{3}}\right) = \dfrac{1}{4}$

Step-by-step explanation:

Given that :

• P(A) = 1/3
• p(B)= 1/5
• P (A U B) = 11/30

To Find :

P (A/B).​

Solution :

As we know :

P (A/B) = P(A ∩ B).

We know that :

The Formula of P(A/B) :

$\bigstar\;\boxed{\sf \dfrac{P(A\cup B)}{P(B)}}$

$\bigstar\;\boxed{\sf p(a\cup b) =p(a)+p(b)-p(a\cap b)}}$

Plug the given values :

$\sf \\\implies \dfrac{1}{2} =\dfrac{1}{4}+\dfrac{1}{3}-p(a \cap b)\\ \\\implies \dfrac{1}{2} =\dfrac{7}{12}-p(a \cap b)\\ \\\implies p(a \cap b)=\dfrac{7}{12}-\dfrac{1}{2}\\ \\\implies p(a \cap b)=\dfrac{1}{12}$

Use the formula :

$\sf \\\implies p\left(\dfrac{a}{b}\right) =\left (\dfrac{\dfrac{1}{12}}{\dfrac{1}{3}}\right)\\ \\\implies p\left(\dfrac{a}{b}\right) =\dfrac{1}{4}$

$\therefore$ $\sf\\ \\\implies P \left(\dfrac{A}{B}\right) = \left (\dfrac{\dfrac{1}{12}}{\dfrac{1}{3}}\right) = \dfrac{1}{4}$