 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says evaluate probability of a union b if twice probability of a is equal to probability of b which is equal to 5 over 13 and probability of a upon b is equal to 2 over 5 Now the condition probability of an event e given the occurrence of the event f is given by probability of e upon f is equal to probability of e intersection f upon probability of f where probability of f is not equal to 0 So this is a key idea behind that question We will take the help of this key idea to solve the above question So let's start the solution now we are given twice probability of a is equal to probability of b which is equal to 5 over 13 and probability of a upon b is equal to 2 over 5 Now according to our key idea we have probability of a upon b is equal to probability of a intersection b upon probability of b Provided probability of b is not equal to 0 So this implies probability of a intersection b is equal to probability of a upon b into probability of b Now we are given probability of a upon b is equal to 2 over 5 probability of b is 5 over 13 So probability of a intersection b is equal to 2 over 5 into 5 over 13 and this is equal to 2 over 13 Again we know that probability of a union b is equal to probability of a plus probability of b minus probability of a intersection b now twice probability of a is equal to 5 over 13 therefore probability of a is equal to 5 over 26 hence probability of a union b is equal to probability of a which is 5 over 26 plus probability of b which is given to us 5 over 13 minus probability of a intersection b which is 2 over 13 and this is equal to 5 plus 10 minus 4 over 26 and this is equal to 15 minus 4 that is 11 over 26 Hence the answer for this question is 11 over 26 I hope the solution is clear to you. Bye and have a nice day