Question

If the probability of winning a game is 0.995 then what will be the probability of losing a game?

Answer 1

Hint: In this type of question we have to use the concept of probability. We know that the probability is a measure of the likelihood of an event to occur. Here we use the concept of complementary event, which is defined as the possibility that there will be only two outcomes which states that an event will occur or not. We know that, the probability of all events in a sample space adds up to 1. Hence, in the case of complementary events we can say that the sum of probability of an event occurring and the probability of an event not occurring is equal to 1.

Complete step by step answer:
Now, we have to find the probability of losing a game, if the probability of winning a game is 0.995.
As we know, the sum of the probability of an event occurring and the probability of an event not occurring is always equal to 1. Hence, we can write,
\[\begin{align}
  & \Rightarrow \text{Probability of winning + Probability of losing = 1} \\
 & \Rightarrow \text{Probability of losing = 1 - Probability of winning} \\
\end{align}\]
Now, as we have given that, the probability of winning a game is 0.995,
\[\begin{align}
  & \Rightarrow \text{Probability of losing = 1 }-0.995 \\
 & \Rightarrow \text{Probability of losing = }0.005 \\
\end{align}\]
Hence, the probability of losing a game is \[0.005\].

Note: In this type of question students have to remember that the sum of all probabilities equal to 1. Also students have to take care in subtraction of decimal numbers. Students have to remember the definition of complementary event and hence they have to note that the winning and losing a game are complementary events of each other.