SOLUTION: In a class, the probability of all the students passing the science examination is 0.8 that of the whole class passing the social studies examination is 0.7 If the probability of t

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Question 664884: In a class, the probability of all the students passing the science examination is 0.8 that of the whole class passing the social studies examination is 0.7 If the probability of the whole class passing at least one of the two exams is 0.95 find the probability of not getting any failures in the whole class in both science and social studies
Answer by kevwill(135) About Me  (Show Source):
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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