Answer :
To solve this problem, we need to find the probability of the complementary event given the probability of the event itself.
### Step-by-Step Solution:
1. Identify the probability of the event:
The probability of the event is given as \(\frac{3}{5}\).
2. Understand the concept of complementary events:
The sum of the probabilities of an event and its complementary event is always equal to 1. Mathematically, this is expressed as:
[tex]\[ P(\text{Event}) + P(\text{Complementary Event}) = 1 \][/tex]
3. Use the given probability to find the complementary probability:
Let \(P(\text{Event}) = \frac{3}{5}\). We need to find \(P(\text{Complementary Event})\).
The formula to find the probability of the complementary event is:
[tex]\[ P(\text{Complementary Event}) = 1 - P(\text{Event}) \][/tex]
4. Substitute the given probability:
[tex]\[ P(\text{Complementary Event}) = 1 - \frac{3}{5} \][/tex]
5. Perform the subtraction:
To subtract \(\frac{3}{5}\) from 1, we can convert 1 into a fraction with the same denominator:
[tex]\[ 1 = \frac{5}{5} \][/tex]
Then, subtract \(\frac{3}{5}\) from \(\frac{5}{5}\):
[tex]\[ \frac{5}{5} - \frac{3}{5} = \frac{2}{5} \][/tex]
6. Simplify the result:
The simplified result is already \(\frac{2}{5}\).
7. Convert the fraction to a decimal (optional):
Although not strictly necessary, converting the fraction \(\frac{2}{5}\) to a decimal can sometimes make the result clearer:
[tex]\[ \frac{2}{5} = 0.4 \][/tex]
Thus, the probability of the complementary event is [tex]\(\frac{2}{5}\)[/tex], which is equivalent to 0.4 in decimal form.
### Step-by-Step Solution:
1. Identify the probability of the event:
The probability of the event is given as \(\frac{3}{5}\).
2. Understand the concept of complementary events:
The sum of the probabilities of an event and its complementary event is always equal to 1. Mathematically, this is expressed as:
[tex]\[ P(\text{Event}) + P(\text{Complementary Event}) = 1 \][/tex]
3. Use the given probability to find the complementary probability:
Let \(P(\text{Event}) = \frac{3}{5}\). We need to find \(P(\text{Complementary Event})\).
The formula to find the probability of the complementary event is:
[tex]\[ P(\text{Complementary Event}) = 1 - P(\text{Event}) \][/tex]
4. Substitute the given probability:
[tex]\[ P(\text{Complementary Event}) = 1 - \frac{3}{5} \][/tex]
5. Perform the subtraction:
To subtract \(\frac{3}{5}\) from 1, we can convert 1 into a fraction with the same denominator:
[tex]\[ 1 = \frac{5}{5} \][/tex]
Then, subtract \(\frac{3}{5}\) from \(\frac{5}{5}\):
[tex]\[ \frac{5}{5} - \frac{3}{5} = \frac{2}{5} \][/tex]
6. Simplify the result:
The simplified result is already \(\frac{2}{5}\).
7. Convert the fraction to a decimal (optional):
Although not strictly necessary, converting the fraction \(\frac{2}{5}\) to a decimal can sometimes make the result clearer:
[tex]\[ \frac{2}{5} = 0.4 \][/tex]
Thus, the probability of the complementary event is [tex]\(\frac{2}{5}\)[/tex], which is equivalent to 0.4 in decimal form.
