What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places

The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Step-by-step explanation:

The complete question is:

There are 103 students in a physics class. The instructor must choose two students at random.

Students in a Physics Class

Academic Year          Physics majors           Non-Physics majors

Freshmen                              17                                     15

Sophomores                         20                                    14

Juniors                                   11                                      17

Seniors                                   5                                       4

What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution:

There are a total of N = 103 students present in a Physics class.

Some of the students are Physics Major and some are not.

The instructor has to select two students at random.

The instructor first selects a senior Physics major and then a sophomore Physics major.

Compute the probability of selecting a senior Physics major student as follows:

Now he two students are selected without replacement.

So, after selecting a senior Physics major student there are 102 students remaining in the class.

Compute the probability of selecting a sophomore Physics major student as follows:

Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:

Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.