There are 40 pupils in a class, 30 of them study biology, 22 study Physics and 21 study chemistry. 15 study Physics and biology, 10 study Physics and chemistry and 13 study biology and chemistry.Each student in the class studies at least one of the three subject.

1.represent the information on a Venn diagram?
2.how many pupils study all the three subject?
3.if a pupils is selected at random, what is the probability that he study Physics or chemistry?

1 answer

The solution

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Venn diagrams can help visually represent data. In this case, we have a class of 40 pupils who study biology, physics, and chemistry. Out of these, 30 study biology, 22 study physics, and 21 study chemistry. There are 15 students who study both physics and biology, 10 study both physics and chemistry, and 13 study both biology and chemistry. Interestingly, each student in the class studies at least one of the three subjects. To answer the questions: 1. A Venn diagram can be used to represent this information, with overlapping circles representing the subjects, and numbers indicating the number of students in each region of overlap. 2. To determine how many pupils study all three subjects, we look at the region where all three circles overlap. By comparing the given data, we can determine this number to be 5 students. 3. If a pupil is selected randomly, the probability that they study Physics or Chemistry can be found by adding the number of students studying each subject (22 + 21 = 43) and subtracting the number who study both (10). Therefore, the probability is 33 out of 40, or 0.825.