In a science class of 120 student ,56 passed physics,61 passed chemistry ,60 passed biology,20 passed both physics and chemistry 24 passed both physics and biology,26 passed both chemistry and biology and 5 passed none of the three subjects. (1). Draw a Venn diagram to show the information.
(2). Find the number of students that passed all the three subject.
(3). Physics only.
(4). Chemistry only.
(5).At least two subject .
(6). At most two subject .
(7). At most three subject.
(8).At least one subject.
Cannot draw diagrams on these posts.
Will the certificate be complete without maths?
It depends on the specific requirements of the certificate or program you are pursuing. Some certificates or programs may require a certain level of math proficiency, while others may not. It's best to check with the institution issuing the certificate or the program coordinator to confirm their specific requirements.
To answer these questions, we can start by drawing a Venn diagram. A Venn diagram is a visual representation of sets, used to show relationships and intersections between different groups or categories.
1. To draw a Venn diagram for this scenario, we will need three circles to represent the subjects: physics, chemistry, and biology. Draw three overlapping circles, one for each subject, with enough space in the middle to represent the overlapping sections.
2. To find the number of students that passed all three subjects, we need to find the overlap in the center of the Venn diagram. From the given information, we know that 56 students passed physics, 61 passed chemistry, and 60 passed biology. Therefore, the number of students that passed all three subjects is the minimum value among these three, which is 20.
3. To find the number of students who passed only physics, we need to find the section that includes physics but not the other two subjects. Starting from the physics circle, subtract the number of students who passed both physics and chemistry (20) and both physics and biology (24). So, 56 - 20 - 24 = 12 students passed only physics.
4. To find the number of students who passed only chemistry, follow the same method. Starting from the chemistry circle, subtract the number of students who passed both physics and chemistry (20) and both chemistry and biology (26). So, 61 - 20 - 26 = 15 students passed only chemistry.
5. To find the number of students who passed at least two subjects, we need to add up the sections where two or three subjects overlap. Add the number of students who passed both physics and chemistry (20), both physics and biology (24), and both chemistry and biology (26). So, 20 + 24 + 26 = 70 students passed at least two subjects.
6. To find the number of students who passed at most two subjects, we need to subtract the number of students who passed all three subjects from the total number of students. From the given information, 5 students passed none of the three subjects. So, 120 - 5 = 115 students passed at most two subjects.
7. To find the number of students who passed at most three subjects, we can simply add up all the sections in the Venn diagram. This includes the students who passed none of the three subjects (5), the students who passed only one subject (12 + 15 = 27), the students who passed at least two subjects (70), and the students who passed all three subjects (20). So, 5 + 27 + 70 + 20 = 122 students passed at most three subjects.
8. To find the number of students who passed at least one subject, we need to subtract the number of students who passed none of the three subjects from the total number of students. From the given information, 5 students did not pass any of the subjects. So, 120 - 5 = 115 students passed at least one subject.