Question

(1) The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?
(2) If the probability of winning a game is 0.6, what is the probability of losing it?
(a) (1) 0.17
       (2) 0.3
(b) (1) 0.15
       (2) 0.4
(c) (1) 0.13
       (2) 0.5
(d) (1) 0.11
       (2) 0.6

Answer 1

Hint: In this question, we need to find the complement events of the given events. Now, we need to subtract the probability of the given event from 1 to get the probability of its complement event.The probability of complement of an event A is given by
\[P\left( A' \right)=1-P\left( A \right)\]

Complete step-by-step answer:
PROBABILITY: If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A, denoted by P(A), is given by
\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favourable outcomes}}{\text{Total number of possible outcomes}}\]
COMPLEMENT OF AN EVENT: Let A be an event in a sample space S, the complement of A is the set of all sample points of the space other than the sample point in A and it is denoted by A'
The probability of complement of an event A is
\[P\left( A' \right)=1-P\left( A \right)\]
Now, from the first part of the question we have
Let us assume that the event of raining tomorrow as A
Now, as given in the question that probability to rain tomorrow
\[\Rightarrow P\left( A \right)=0.85\]
Now, the event of not raining tomorrow is the complement of event A
Let us now find its probability from the above formula of probability of a complement event
\[\Rightarrow P\left( A' \right)=1-P\left( A \right)\]
Now, on substituting the respective value we get,
\[\begin{align}
  & \Rightarrow P\left( A' \right)=1-0.85 \\
 & \therefore P\left( A' \right)=0.15 \\
\end{align}\]

Now, from the second part of the question we have
Let us assume that the event of winning the game as B
Now, as already given in the question that the probability of winning the game is
\[\Rightarrow P\left( B \right)=0.6\]
Now, the event of losing the game is the complement of event B
Let us now find its probability from the above formula of probability of a complement event
\[\Rightarrow P\left( B' \right)=1-P\left( B \right)\]
Now, on substituting the respective value we get,
\[\Rightarrow P\left( B' \right)=1-0.6\]
Now, on further simplification we get
\[\therefore P\left( B' \right)=0.4\]
Hence, the correct option is (b).

Note: It is important to note that the given events are complement events as not is mentioned which means one event is exactly opposite to the other. So, that we can directly find its probability by equating their sum to one.While substituting the values we should not commit any of the calculation mistakes because it changes the result and so the option.