Question

If the difference between the probability of success and failure of an event is 5/19. Find the probability of success and failure of the event

Answer 1

Answer:

Let X denote the probability of success and Y denote the probability of failure

ATQ X - Y = 5/19

We Know that X + Y = 1

By adding both the equations

X - Y + X + Y = 5/19 + 1

2X = 5/19 + 19/19

2X = 24/19

X = 24/38 = 12/19

X + Y = 1

12/19 - 1 = Y

12/19 - 19/19 = Y

7/19 = Y

Answer 2

Answer:

The probability of success = 12/19

The probability of failure  = 7/19

Step-by-step explanation:

Given that the difference between the probability of success and failure of an event  = 5/19

let the probability of success = P(E)

      the probability of failure   = P(E')

we know that in an event, sum of the probability of success and failure is equals to 1

⇒ P(E) + P(E') = 1  _ (1)

from given data  P(E) -P(E') = 5/19 _ (2)

add  (1) and (2) ⇒  P(E) + P(E') +P(E) -P(E') = 1+ $\frac{5}{19}$

                        ⇒  2P(E) = 24 / 19

                        ⇒ 19(P(E)) = 24 /2

                        ⇒ 19P(E) = 12

                        ⇒ P(E) = 12/19

P(E) =12/19  substitute in (1) ⇒ 12/19 + P(E') = 1

                                            ⇒ P(E') = 1-12/19

                                            ⇒ P(E') = 7/19