# What is the probability of an impossible event?

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Hint- Probability is defined as the ratio of number of favorable outcomes to the total number of outcomes. For an impossible event the total number of favorable outcomes is zero.

Since, we know that for an impossible event number of favorable outcomes $ = 0$

So, the probability of an impossible event is

$

= \dfrac{{{\text{number of favorable events}}}}{{{\text{total number of events}}}} \\

= \dfrac{0}{{{\text{total number of events}}}} \\

= 0 \\

$

Therefore the probability of an impossible event is zero.

Note- Probability exists on a scale from $0{\text{ to 1}}$ , with $0$being defined as an impossible event

and being $1$defined as a sure event. Everything between $0{\text{ and 1}}$ is possible and with

increasing probability, events become more likely.

Since, we know that for an impossible event number of favorable outcomes $ = 0$

So, the probability of an impossible event is

$

= \dfrac{{{\text{number of favorable events}}}}{{{\text{total number of events}}}} \\

= \dfrac{0}{{{\text{total number of events}}}} \\

= 0 \\

$

Therefore the probability of an impossible event is zero.

Note- Probability exists on a scale from $0{\text{ to 1}}$ , with $0$being defined as an impossible event

and being $1$defined as a sure event. Everything between $0{\text{ and 1}}$ is possible and with

increasing probability, events become more likely.

Last updated date: 23rd Sep 2023

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