Given:
The two statements.
To find:
The probability of an impossible event.
The probability of a certain event.
Solution:
Formula for probability is:
[tex]P=\dfrac{\text{Possible favorable outcomes}}{\text{Total number of outcomes}}[/tex]
For an impossible event, the possible favorable outcomes is 0. So,
[tex]P=\dfrac{0}{\text{Total number of outcomes}}[/tex]
[tex]P=0[/tex]
For a certain event (sure event), the possible favorable outcomes is equal to total number of outcomes. So,
[tex]P=\dfrac{\text{Total number of outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]P=1[/tex]
Therefore, an event that is impossible has probability 0 and an event that is certain has probability 1.
