Question

I want to know how to get the answer which is “3/10” can anyone tell me the steps to solving this probability problem?

Answer 1

Answer: Probability that a random chosen adult run or swims is given by

$\frac{3}{10}$

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,

$P(A)=\frac{22}{80}=\frac{11}{40}\\\\P(B)=\frac{18}{80}=\frac{9}{40}\\\\P(A\cap B)=\frac{1}{5}$

As we know the formula , i.e.

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=\frac{11}{40}+\frac{9}{40}-\frac{1}{5}\\\\P(A\cup B)=\frac{11+9}{40}-\frac{1}{5}\\\\P(A\cup B)=\frac{20}{40}-\frac{1}{5}\\\\P(A\cup B)=\frac{1}{2}-\frac{1}{5}\\\\P(A\cup B)=\frac{5-2}{10}=\frac{3}{10}$

Hence, Probability that a random chosen adult run or swims is given by

$\frac{3}{10}$