Question

Find the indicated conditional probability

Answer 1

Given:

The two way table.

To find:

The conditional probability of P(Drive to school | Senior).

Solution:

The conditional probability is defined as:

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

Using this formula, we get

$P(\text{Drive to school }|\text{ Senior})=\dfrac{P(\text{Drive to school and senior})}{P(\text{Senior})}$                      ...(i)

From the given two way table, we get

Drive to school and senior = 25

Senior = 25+5+5

           = 35

Total = 2+25+3+13+20+2+25+5+5

         = 100

Now,

$P(\text{Drive to school and senior})=\dfrac{25}{100}$

$P(\text{Senior})=\dfrac{35}{100}$

Substituting these values in (i), we get

$P(\text{Drive to school }|\text{ Senior})=\dfrac{\dfrac{25}{100}}{\dfrac{35}{100}}$

$P(\text{Drive to school }|\text{ Senior})=\dfrac{25}{35}$

$P(\text{Drive to school }|\text{ Senior})=0.7142857$

$P(\text{Drive to school }|\text{ Senior})\approx 0.71$

Therefore, the required conditional probability is 0.71.

Answer 2

Answer:

.71

Step-by-step explanation: