The probability that it will rain today is 0.84. What is the probability that it will not rain today?
Answer
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Hint: Use the fact that the sum of probability of occurrence of an event and probability of non-occurrence of an event is 1. Subtract the probability of raining today from 1 to get the probability of not raining today.
Complete step-by-step answer:
We know that the probability of raining today is 0.84. We have to calculate the probability of not raining today.
We know that the sum of probability of occurrence of an event and probability of non-occurrence of an event is 1.
Let us denote the event of getting a rain by A and not getting a rain by \[{{A}^{c}}\]. Thus, we have \[P\left( A \right)+P\left( {{A}^{c}} \right)=1\].
We know that \[P\left( A \right)=0.84\].
To find the probability of not getting a rain, we will subtract the probability of getting a rain from 1.
Thus, we have \[P\left( {{A}^{c}} \right)=1-P\left( A \right)\].
Substituting the value \[P\left( A \right)=0.84\] in the above equation, we have \[P\left( {{A}^{c}} \right)=1-P\left( A \right)=1-0.84\].
So, we have \[P\left( {{A}^{c}} \right)=1-0.84=0.16\].
Hence, the probability of not raining today is 0.16.
Note: Probability of any event describes how likely an event is to occur or how likely it is that a proposition is true. The value of probability of any event always lies in the range \[\left[ 0,1 \right]\] where having 0 probability indicates that the event is impossible to happen, while having probability equal to 1 indicates that the event will surely happen. We must remember that the sum of probability of occurrence of some event and probability of non-occurrence of the same event is always 1. We can’t solve this question without using the fact that the sum of probability of occurrence of an event and probability of non-occurrence of an event is 1.
Complete step-by-step answer:
We know that the probability of raining today is 0.84. We have to calculate the probability of not raining today.
We know that the sum of probability of occurrence of an event and probability of non-occurrence of an event is 1.
Let us denote the event of getting a rain by A and not getting a rain by \[{{A}^{c}}\]. Thus, we have \[P\left( A \right)+P\left( {{A}^{c}} \right)=1\].
We know that \[P\left( A \right)=0.84\].
To find the probability of not getting a rain, we will subtract the probability of getting a rain from 1.
Thus, we have \[P\left( {{A}^{c}} \right)=1-P\left( A \right)\].
Substituting the value \[P\left( A \right)=0.84\] in the above equation, we have \[P\left( {{A}^{c}} \right)=1-P\left( A \right)=1-0.84\].
So, we have \[P\left( {{A}^{c}} \right)=1-0.84=0.16\].
Hence, the probability of not raining today is 0.16.
Note: Probability of any event describes how likely an event is to occur or how likely it is that a proposition is true. The value of probability of any event always lies in the range \[\left[ 0,1 \right]\] where having 0 probability indicates that the event is impossible to happen, while having probability equal to 1 indicates that the event will surely happen. We must remember that the sum of probability of occurrence of some event and probability of non-occurrence of the same event is always 1. We can’t solve this question without using the fact that the sum of probability of occurrence of an event and probability of non-occurrence of an event is 1.
Last updated date: 21st Sep 2023
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