Question 664884
Let's all the students passing the science examination Event A, and all the students passing the social studies examination Event B.  The probability that the entire class passed at least one of the exams is P(A∪B).  The probability that the entire class passed both exams is P(A∩B).
  
P(A) = 0.8
P(B) = 0.7
P(A∪B) = 0.95
  
And by definition P(A∪B) = P(A) + P(B) - P(A∩B), so
P(A∪B) = P(A) + P(B) - P(A∩B)
0.95 = 0.8 + 0.7 - P(A∩B)
0.95 = 1.5 - P(A∩B)
-P(A∩B) = 0.95 - 1.5
P(A∩B) = 0.55
 
So the probability that the entire class passed both exams is 0.55