Question

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

Answer 1

Answer:

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:

$P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}$

                                        $=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485$

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:

$P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}$

                                        $=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961$

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

$P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})$

                                     $=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095$

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