Question

In a game, we roll a fair die. If we roll an odd number, we lose and we win if we roll an even number. We are interested in computing the probability of losing this game. Which of the following is the desired outcome and the favorable outcome respectively?

• A. $P\left(Winning\right)$, $P\left(Losing\right)$
• B. $P\left(Losing\right)$, $P\left(Winning\right)$
• C. $P\left(Losing\right)$, $P\left(Losing\right)$
• D. $P\left(Winning\right)$, $P\left(Winning\right)$

Answer 1

The correct option is A $P\left(Winning\right)$, $P\left(Losing\right)$

The term "favorable outcome" does not necessarily mean that the outcome is desirable – in some experiments, the favorable outcome could be the failure of a test or the occurrence of an undesirable event.

We are interested in calculating the probability of losing the game. Hence, $P\left(losing\right)$ is the favorable outcome. We would always like to win a game and hence $P\left(winning\right)$ is the desirable outcome.