ANSWER: 1/6
Step-by-step explanation:
A fairly basic and fundamental problem in Probability, but still worth doing as an example of good mathematics.
Assumptions
The number cube is fair, that is not biased in any manner.
Key Points to Note.
Each roll of the number cube is an Independant Event, that is the outcome of any toss has no impact whatsoever on the outcome of any other toss.
The Probability of NOT achieving a specific outcome is equivalent TO ACHIEVING all other outcomes.
The Probability of achieving two sequential outcomes, is the Probability of achieving the first outcome multiplied by the Probability of achieving the second.
Analysis
What is the probability of rolling a 3 on a 6-sided number cube and then NOT rolling a 3 on a 6-sided number cube?
There are 6 sides on the number cube, each with an equal probability of being a specific outcome.
Therefore the Probability of a 3 as the outcome, is ( 1/6 ).
What is the probability of NOT rolling a 3 on a 6-sided number cube?
The Probability of NOT rolling a 3, is the same as either 1 - Probability (3) or Probability (1, 2, 4, 5, 6), which is equivalent to ( 5/6 )
Sequential Probabilities.
What is the probability of rolling a 3 on a 6-sided number cube AND THEN NOT rolling a 3 on a 6-sided number cube?
P( 3 ) then P( Not a 3 ) = ( 1/6 ) * ( 5/6 ) which equals ( 5/36 )
A Further Point to Note
Because the two rolls of the number cube are independant, the final probability is independant of the order of which outcome is first sought.
