Answer: Probability that a random chosen adult run or swims is given by
[tex]\frac{3}{10}[/tex]
Explanation:
Since we have given that
Number of adults surveyed = 80
Number of adults regularly run for exercise = 22
Remaining number of adults regularly swims for exercise =18
Now, Let Event A : getting adults run for exercise
Event B : getting adults swims for exercise
So,
[tex]P(A)=\frac{22}{80}=\frac{11}{40}\\\\P(B)=\frac{18}{80}=\frac{9}{40}\\\\P(A\cap B)=\frac{1}{5}[/tex]
As we know the formula , i.e.
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=\frac{11}{40}+\frac{9}{40}-\frac{1}{5}\\\\P(A\cup B)=\frac{11+9}{40}-\frac{1}{5}\\\\P(A\cup B)=\frac{20}{40}-\frac{1}{5}\\\\P(A\cup B)=\frac{1}{2}-\frac{1}{5}\\\\P(A\cup B)=\frac{5-2}{10}=\frac{3}{10}[/tex]
Hence, Probability that a random chosen adult run or swims is given by
[tex]\frac{3}{10}[/tex]
