Question

Find the indicated conditional probabilityusing the following two-way table:GradeDrive to schoolTake the busWalkSophomore2253Junior13202Senior2555P( Take the bus | Senior ) = [?]

Answer 1

This problem is about conditional probability, where:

P(A | B) = Probability of A given B

P(A ∩ B) = Probability of A and B

P(B) = Probability of B

And the relation with the terms above is:

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

In order to calculate de probabilities we need to sum over the students:

Total number of students = 100 (we just sum all the numbers in the table)

Now, the events are:

A = take the bus

B = be a senior student

P(A ∩ B) = # of senior students that take the bus / total number of students = 5 / 100 = 0.05

P(B) = # of senior students / total number of students = 35 / 100 = 0.35

So, using the formula of above:

$P(A\text{ | B) = }\frac{P(A\text{ }\cap\text{ B)}}{P(B)}\text{ = }\frac{0.05}{0.35}\text{ = }\frac{1}{7}=0.142857$

Or:

$P(A|B)\text{ = 14.29 \%}$