Question

Below, the two-way table is given for a classof students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female 3463TotalIf a female student is selected at random, find theprobability that the student is a senior.

Answer 1

Conditional Probability

First, we must complete the totals in the table as follows:

The formula for the conditional probability is:

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

Where A is an event we know has already occurred, B is an event we want to calculate its probability of occurrence, and P∩A is the probability of both occurring.

We know a female student has been selected, so that is our known event and:

`P(A)=(16)/(30)=(8)/(15)`

The probability that a female student is also a senior is:

`P(A\cap B)=(3)/(30)=(1)/(10)`

Substituting:

`\begin{gathered} P(B|A)=((1)/(10))/((8)/(15)) \\ \\ P(B\lvert\rvert A)=(1)/(10)(15)/(8)=(3)/(16) \end{gathered}`

The required probability is 3/16