Question

If the difference between the probability of success and failure of an event is 4/13. Find the probability of success and failure of the event.​

Answer 1

see the attached pic for answer

Answer 2

Given :-

♦ The difference between the probability of success and failure of an event is 4/13

To find :-

♦ The probability of success and failure of the event .

Solution :-

Let the probability of success of an event be P(S)

Let the probability of failure of the event be P (F)

They are complementary events.

So, P(S) + P(F) = 1 --------------(1)

Given that

The difference between the probability of success and failure of the event = 4/13

=> P(S) - P(F) = 4/13 -----------(2)

On adding (1) & (2) then

P(S) + P(F) = 1

P(S) - P(F) = 4/13

(+)

_______________

2 P(S) + 0 = 1+(4/13)

_______________

=> 2 P(S) = 1+(4/13)

=> 2 P(S) = (13+4)/13

=> 2 P(S) = 17/13

=> P(S) = (17/13)/2

=> P(S) = 17/26

On substituting the value of P(S) in (1)

=> (17/26)+P(F) = 1

=> P(F) = 1-(17/26)

=> P(F) = (26-17)/26

=> P(F) = 9/26

Therefore, P(S) = 17/26 and P(F) = 9/26

Answer :-

The Probability of success of the event = 17/26

The Probability of failure of the event = 9/26

Used formulae:-

♦ The sum of the probabilities of the two complementary events in a trial is 1.

♦ If the probability of an event E is P(E) then P(E) + P(not E) = 1.