2 Answers

Anjali A · Answer 1 · 2022-09-11T10:51:42+0000

Given:

The two way table.

To find:

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

Solution:

The conditional probability is defined as:

$P(A|B)=(P(A\cap B))/(P(B))$

Using this formula, we get

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

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

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

Substituting these values in (i), we get

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

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

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

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

Therefore, the required conditional probability is 0.71.

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