Question

if event A is the subset of b the probability of p(A/B) is equal to​

Answer 1

$\displaystyle \sf{P\bigg( \frac{A}{B}\bigg) = \frac{P(A)}{P(B)} }$

Correct question : if event A is the subset of B the probability of P(A/B) is equal to

Given :

The event A is the subset of B

To find :

The probability of P(A/B)

Solution :

Step 1 of 2 :

Define subset

A set A is said to be a subset of B if every element of A is an element of B . It is written as A ⊆ B

Step 2 of 2 :

Find the value of P(A/B)

Since the event A is the subset of B

∴ A ⊆ B

⇒ A ∩ B = A

Thus we get ,

$\displaystyle \sf{P\bigg( \frac{A}{B}\bigg) }$

$\displaystyle \sf{ = \frac{P(A \: \cap \:B )}{P(B)}}$

$\displaystyle \sf{ = \frac{P(A )}{P(B)}}\: \: \: \: \: \bigg[ \: \because \: A \: \cap \:B = A \: \bigg]$

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Answer 2

p(A/B) = p(A)/p(B)

Given

• A is the subset of b

• To find
• the probability of p(A/B) is equal to

Solution

we are provided that event A is subset of event B.

we know that when a set a is subset of a another set B then

all the elements of set A should be present in the set B.

therefore, we arrive at a conclusion that A intersection B would mean A.

A∩ B = A ( As A is present in set B) ....equ1.

we also know that ,

p(A/B) = p(A∩ B)/p(B)

substitute the value obtained in the equation 1 to the above equation that we are familiar with, we get,

p(A∩ B) = p(A)

or,

p(A/B) = p(A)/p(B)

Therefore our final answer would be,

p(A/B) = p(A)/p(B)

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