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# Math Examples of Addition Theorem

• ## The probability of the students studying in Engineering is 40, and in medical is 50, and there are 20 students who study both, find the total number of students in the class?

For solving this type of problem, we need to have good knowledge of Addition Theorem of Probability. According to addition theorem, if we have two Mutually Exclusive Events then we can find the Union of all the event by the formula given below:
P(A ∪B) = P(A) +P(B)- P(A∩B)
If we talk about our question we have  number of Students who like Engineering  so the probability will be P(A) = 30 and the number of  students who like medical are  40 so P(B) = 40 and the number of students who like both Engineering and medical  are 12 so P(A∩B) = 12 , our task is to find the number of students in the class which can be find easily by determining P(A ∪B), so by the additional formula,
P(A ∪B) = 40 + 50 – 20,
P(A ∪B) = 70, So the total number of students in the class is 70.

## The probability of students studying math is 30, of science is 40, and there are 12 students who study both, find the total number of student in the class?

For solving this type of problem, we need to have good knowledge of Addition Theorem of Probability. According to addition theorem, if we have two Mutually Exclusive Events then we can find the Union of the entire event by the formula given below:
P (A ∪B) = P (A) +P (B) - P (A∩B)
If we talk about our question we have number of Students who like Math so probability will be P(A) = 30 and the number of  students who like Science are  40 so P(B) = 40 and the number of students who like both math and science are 12 so P(A∩B) = 12 , our task is to find the number of students in the class that we can find by finding P(A ∪B), so by the additional formula,
P (A ∪B) = 40 + 30 – 12
P (A ∪B) = 58
So the total number of student in the class is 58.

## In a class there are 50 students, twenty students like playing cricket and ten students like playing football. Find the probability of student who like both football and cricket?

For solving this type of problem, we need to have good knowledge of Addition Theorem of Probability. According to addition theorem, if we have two Mutually Exclusive Events then we can find the Union of the entire event by the formula given below:
P (A ∪B) = P (A) +P (B) - P (A∩B)
Here P (A) is the probability of first event and P (B) is probability of second event , P(A∩B) is the probability  of Intersection of both the event and P(A ∪B) is probability of union of both the event.
If we talk about our question we have number of students who like cricket so probability will be P (A) = 20 and the number of  students who like football are twenty so P(B) = 10 and the number of students in the class is 50 so P(A ∪B) = 50. Now, if we see our formula only one thing is unknown that is P(A∩B), so by putting all the values we can  find the value of P(A∩B).
50 = 20 + 10 - P (A∩B)
Now we will take P (A∩B) to right side so there will be a change in sign,
P (A∩B) = 30 – 50
P (A∩B) = -20
There is no meaning of minus sign here, so the players who play both football and cricket are 20.
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