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

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

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}`

`=(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}`

`=(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})* P(\text{Sophomore})`

`=0.0485* 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.