Conditional Probability

Conditional probability : 
let's say there are two events A and B and we know that Event A has already occurred then what is the probability of occurring if B?

 P(A/B)=  P(A∩B)  /  P(B) 

For example: 

When we roll a dice what is the probability of getting a prime number when it is already known that an even no is shown up?

Solution:- 

let's say A is an event of getting an even no and B is an event of getting a prime number So

Method 1:-

P(B /A) =P(B ∩ A)  /  P(A)

Sample space = {1,2,3,4,5,6}

E(A)={2,4,6}

P(A)= 3/6 =1/2

for B Sample space is = {2,4,6}

So E(B)= {2}

P(B)= 1/3

Method 2:

P(A)= 1/2

E(A ∩ B) = {2}

P( E∩ B) = 1/6

So 

P(B/A) = (1/6) / 1/2 = 1/3 

 

We will see more example of conditional probabilities.

 

 

 

 

 

0Comment