Question

Solve the question

in a group of 65 students 40students want to be a doctor and 20 wants to be a social worker. the number of students who want to be a doctor only and the student who wants to be a social worker only are in the ratio 3:1 by drawing venn diagram find.
1)how many students want to both?
2)how many want to be both?​

Answer 1

Answer:To find the number of students who want to be both a doctor and a social worker, we can use the Principle of Inclusion-Exclusion (PIE). This principle states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.

So, the number of students who want to be both a doctor and a social worker can be calculated as:

|Doctor ∩ Social worker| = |Doctor| + |Social worker| - |Doctor U Social worker|

|Doctor ∩ Social worker| = 40 + 20 - 65

|Doctor ∩ Social worker| = -5

However, this result is negative which is not possible, therefore, no students want to be both a doctor and a social worker.

To find the number of students who want to be both, we have to find the number of students who want to be both a doctor and a social worker which is 0 in this case.

Explanation: