Question

Which of the following statement(s) is(are) true?

• A. Probability of a certain event is $1$
• B. Probability of an impossible event is $0$
• C. Probability of an event cannot be negative
• D. Probability of an event can be negative

Answer 1

Answer: (A), (B), (C)

Probability of an event cannot be negative

$\underset{–}{\text{Certain Events}:}$
Events whose occurrence is $100\%$ sure, those events are called certain events. The probability of such an event is $\underset{–}{always1.}$
For example, the probability of getting a number between $1$ to $6$ when rolling a die is a certain event.

$\underset{–}{\text{Impossible Events}:}$
An event which is impossible to occur, is called an impossible event. The probability of impossible event is $\underset{–}{always0.}$
For example, In flipping a coin once, an impossible event would be getting both head and tail.

$\bullet$ The probability of an event cannot be a negative number. This is because of the number of outcomes favorable to an event $\left(E\right)\le$ Number of all possible outcomes. So, $0\le P\left(E\right)\le 1$