Question

if probability of happening of an event is 2/7, then find the probability of non-happening of this event.​

Answer 1

Let P(E) be the occurrence of an event

To find the chance of the event not happening at all

Given that P(E)=2/7

According to the law of probability,

P(E)+P(Ē)=1

→P(Ē)=1-P(E)

$\implies \: \sf{1 - \dfrac{2}{7} = \dfrac{5}{7} }$

★Probability of the event not happening is 5/7

Answer 2

» Probability of happening of an event is 2/7.

P(E) = $\frac{2}{7}$

_______ [GIVEN]

• We have to find probability of not happening of event.

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We know that

P(E) + P(Ē) = 1 ____ (eq 1)

Here..

• P(E) is probability of happening of event.

• P(Ē) is probability of not happening of event.

Now put the value in (eq 1)

=> $\frac{2}{7}$ + P(Ē) = 1

=> P(Ē) = 1 - $\frac{2}{7}$

=> P(Ē) = $\frac{7\:-\:2}{7}$

=> P(Ē) = $\frac{5}{7}$

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Probability of not happening of event is $\dfrac{5}{7}$

__________ $\bold{[ANSWER]}$

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✡ More information :

P(E) = $\frac{Number\:of\: favourable\:outcomes}{Total\:number\:of\: outcomes}$

Probability of every sure event is 1 and of impossible event is 0.

The sum of the probabililites of all elementary events of experiment is 1.

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