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Conditional Probability Calculator
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In statistical point of view, conditional probability is nothing but the probability of an event happen provided that another event is already happened before. To find out the conditional probability, we use the online conditional probability calculator. It is denoted as $P$ $(\frac{A}{B})$ (read as probability of $A$ given $B$) if the events are dependent. If they are independent, the notation become simply $P(A)$. The formula to calculate the conditional probability when the events are dependent is given below.
$P$ $(\frac{A}{B})$ = $\frac{P(A\ \cap\ B)}{P(B)}$

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

Where $P$ $(\frac{A}{B})$ is the conditional probability
      
 $P(A)$ is the probability of event $A$
      
 $P(B)$ is the probability of event $B$
 

Steps for Conditional Probability Calculator

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Step 1 :  

Find out the values P(A$\cap$ B) and P(A) or P(B) from the question.




Step 2 :  

Determine the conditional probability using the given equations.

P(A/B)=$\frac{P(A\cap B)}{P(B)}$

P(B/A)=$\frac{P(A\cap B)}{P(A)}$



Problems on Conditional Probability Calculator

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  1. The probability of occurrence of two events A and B is given by 0.25. The probability of occurrence of the event A and that of B is given 0.42 and 0.60 respectively. Calculate the P(A/B) and P(B/A)?


    Step 1 :  

    P(A)=0.42, P(B)=0.60 and P(A$\cap$B)=0.25



    Step 2 :  

    P(A/B)=$\frac{P(A\cap B)}{P(B)}$


    P(A/B)=$\frac{0.25}{0.60}$=0.4166


    P(B/A)=$\frac{P(A\cap B)}{P(A)}$


    P(B/A)=$\frac{0.25}{0.42}$=0.5952



    Answer  :  

    P(A/B)=0.4166

    P(B/A)=0.5952



  2. P(A)=0.65, P(B) and P(A$\cap$B)=0.15. Determine the values of P(A/B) and P(B/A)?


    Step 1 :  

    From the question, it is given that


    P(A)=0.65, P(B) and P(A$\cap$B)=0.15



    Step 2 :  

    P(A/B)=$\frac{P(A\cap B)}{P(B)}$


    P(A/B)=$\frac{0.15}{0.40}$=0.375


    P(B/A)=$\frac{P(A\cap B)}{P(A)}$


    P(B/A)=$\frac{0.15}{0.65}$=0.2307



    Answer  :  

    P(A/B)=0.375

    P(B/A)=0.2307



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