Question

The product of the probabilities of happening of an event E and non-happening of an event is 6/ 25. Find the probability of happening of the event E.

Answer 1

Answer:

Let 'p' denote the probability of happening of an event.

and 'q' denote the probability of not happening of an event.

we are given p×q=$\dfrac{6}{25}$

also we know that q=1-p

p×(1-p)=$\dfrac{6}{25}$

this means that

$p-p^2=\dfrac{6}{25}$

$p^{2}-p+\dfrac{6}{25}=0$

on solving the following quadratic equation:

$\dfrac{25p^2-25p+6}{25}=0$

$25p^2-25p+6=0$

Hence, on solving using the quadratic formula

(

That for any general quadratic equation of the type:

$ax^2+bx+c=0$

the solution is given as:

$x=\dfrac{-b+\sqrt{b^2-4ac} }{2a}, x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}$ )

so, the value of p is:

$p=\dfrac{3}{5}, p=\dfrac{2}{5}$

so, the possibility of happening of an event is either

$\dfrac{3}{5}$  or  $\dfrac{2}{5}$