19. In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is and the probability of passing the second examination is . The probability of passing atleast one of them is . What is the probability of passing both?
Let A be the event that the student passes the first examination and B be the event that the students passes the second examination.
P(A B) is probability of passing at least one of the examination.
P(A B) = 0.95 , P(A)=0.8, P(B)=0.7
P(A B) = P(A)+ P(B) - P(A B)
P(A B) = 0.8 + 0.7 - 0.95 = 1.5 -0.95 = 0.55
Hence,the probability that the student will pass both the examinations is 0.55