Question

if the difference between probability of success and failure of an event is 3/13 . find the probability of success and failure of the event .

Answer 1

let P(s) is the probability of success and
P(f) is probability of failure.
given
P(s) - P(f) = 3/13 -----------------------(1)
we know
P(s) + P(f) = 1 -----------------------(2)
add equation (1) and (2)
2P(s) = 1 + 3/13
2P(s) = 16/13
P(s) = 8/13
put the value of P(s) is in equation (1) 
8/13 - P(f) = 3/13
P(f) = 8/13 - 3/13
P(f) = 5/13
 

Answer 2

let p(E) be the probability of getting success.
let p(notE) be the probability of getting failure.
given that,
         p(E) - p(notE) = 3/13  ⇒1
 we know that 
          p(E)+ p(notE) = 1
   2p(E)=1+(1/3)
 2p(E) =16/13
p(E)=8/13
substitute p(E)in EQ 1
8/13-p(notE) = 3/13
p(notE)=8/13-3/13
p(notE)=5/13
⇒probability of getting success is 8/13
⇒probability of getting failure is 5/13