Question

the table shows the results from a survey that asked 100 adults if they had a high school diploma and if their annual income was more than $30,000.what is the probability that the person has a high school diploma and makes 30,000 or less?

Answer 1

Let A be the event that the person has a high school diploma and let B be the event that the person makes 30000 or less .

Recall that this probability is

`P(A\cap B)`

To calculate this, we will proceed as follows:

The event A refers to the rows of the table and event B refers to the columns of the table.

Note that event A says that the person has a high school diploma. So we will focus only on the first row of the table. Now, the event B says that the person earns more than 30.000 so we should take a look at the second column only.

Since we want to calculate the probability of A and B, we want both events to occur, that is we first find the number of people that is in the first row and the second column. This number is 21.

now, to calculate the probability, we should divide this number by the total amount of people in the survey. That is 100. So the probability we want is

`P(A\cap B)=(21)/(100)`