At an examination, students can select three subjects out of many subjects. The following information is given on the subjects STATS and IT and MATHS.
45% of all students take MATHS
20% take IT and STATS but not MATHS
5% take IT and MATHS but not STAT
90% take at least one of STATS, IT and MATHS
10% take STATS and MATHS but not IT
20% take only MATHS
50% take STAT
What is the percentage of students who take STATS and MATHS and IT.
Becomes real simple if you use Venn diagrams
I placed x in the intersection of M, I, and S. ( x will be the solution to your question)
I filled in the following:
10% take STATS and MATHS but not IT
5% take IT and MATHS but not STAT
20% take only MATHS
I then used: 45% of all students take MATHS
to form the equation
x+10+5+20 = 45
x = 10
Thanks Reiny
To find the percentage of students who take STATS, MATHS, and IT, we need to use the principle of inclusion and exclusion.
Let's define the following variables:
M = Percentage of students taking MATHS
S = Percentage of students taking STATS
I = Percentage of students taking IT
SMS = Percentage of students taking STATS and MATHS but not IT
SIS = Percentage of students taking STATS and IT but not MATHS
MIS = Percentage of students taking MATHS and IT but not STATS
SIM = Percentage of students taking STATS, IT, and MATHS
According to the given information, we have:
M = 45%
SIS = 5%
SMS = 10%
SIM = ? (what we need to find)
Using the principle of inclusion and exclusion, we can set up the equation:
M + S + I - (SIS + SMS + MIS) + SIM = 90%
Now let's substitute the given values into the equation:
45% + 50% + I - (5% + 10% + MIS) + SIM = 90%
Simplifying the equation:
95% + I - MIS + SIM = 90%
Subtracting 95% from both sides:
I - MIS + SIM = -5%
Since the percentage cannot be negative, we can conclude that the equation has no solution. Therefore, we cannot determine the percentage of students who take STATS, MATHS, and IT based on the given information.
To find the percentage of students who take STATS, MATHS, and IT, we need to break down the given information and use the principle of inclusion-exclusion.
Let's use the following symbols to represent the given information:
- P(M) represents the percentage of students who take MATHS.
- P(IT) represents the percentage of students who take IT.
- P(STATS) represents the percentage of students who take STATS.
Now, let's go step by step to find the required percentage:
1. We know that 45% of all students take MATHS: P(M) = 45%.
2. The percentage of students who take IT and STATS but not MATHS is 20%. Let's denote it by P(IT and STATS) but not M. Since this percentage is not given directly, we can find it by subtracting the given information about other categories:
- We know that 90% take at least one of STATS, IT, and MATHS, so the percentage of students who don't take any of these subjects is 100% - 90% = 10%.
- P(IT and STATS) but not M = P(IT and STATS) - P(IT and STATS and M) - P(IT and STATS and not M).
Now, let's find P(IT and STATS and M) and P(IT and STATS and not M):
- We know that 5% take IT and MATHS but not STATS: P(IT and M) and not STATS = 5%.
- We know that 10% take STATS and MATHS but not IT: P(M and STATS) and not IT = 10%.
Using these values, we can calculate P(IT and STATS) but not M:
P(IT and STATS) but not M = P(IT and STATS) - P(IT and STATS and M) - P(IT and STATS and not M)
= P(IT and STATS) - P(IT and M) and not STATS - P(M and STATS) and not IT.
3. We are given that 20% take only MATHS: P(M) and not (IT or STATS) = 20%.
4. We know that 50% take STATS: P(STATS) = 50%.
5. We can use the principle of inclusion-exclusion to calculate P(IT and STATS and M):
P(IT and STATS and M) = P(IT and STATS) - P(IT and STATS) but not M.
Now, let's put all the information together and calculate the percentage of students who take STATS, MATHS, and IT:
P(IT and STATS and M) = P(IT and STATS) - P(IT and STATS) but not M
= P(IT and STATS) - (P(IT and M) and not STATS - P(M and STATS) and not IT).
To find P(IT and STATS), we can use the given information:
P(IT and STATS) = P(IT and STATS and M) + P(IT and STATS and not M)
= P(IT and STATS and M) + P(IT and STATS) but not M
Now, we have the values of P(M), P(IT), P(STATS), P(IT and STATS), P(IT and STATS) but not M, P(IT and M) and not STATS, P(M and STATS) and not IT.
Using these values, we can calculate P(IT and STATS and M) and the final percentage of students who take STATS, MATHS, and IT.