Question

# There are 71 students in a nutrition class. The instructor must choose two students at random....

There are 71 students in a nutrition class. The instructor must choose two students at random.

Students in a Nutrition Class
Academic Year Nutrition majors non-Nutrition majors
Freshmen 17 5
Sophomores 4 5
Juniors 17 16
Seniors 3 4

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

Total number of students in nutrition class = 71

We need to find the probability that on random selection from these students, first a senior Nutrition major and then a sophomore Nutrition major are chosen.

From the table observe that there are 3 senior Nutrition majors and 4 sophomore Nutrition majors.

So first, the probability of selecting a senior Nutrition major = 3/71 then there are rest 70 students left in the class from which we have 4 options to choose so 4/70

Hence , probability that on random selection from these students, first a senior Nutrition major and then a sophomore Nutrition major are chosen = (3/71) x (4/70) = 12/4970 = 0.002414486922 = 0.0024 (rounded to four decimal places)

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