# 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 0.8 and the probability of passing the second examination is 0.7. The probability of passing atleast one of them is 0.95. 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 ( is probability of passing at least one of the examination

Then, P(AB)= 0.95 , P(A)=0.8, P(B)=0.7

P(AB)=P(A) + P(B)-P(AB)

0.95 = 0.8 + 0.7 - P(AB)

P(AB)=1.5-0.95=0.55

0.55 is the probability that student will pass both the examinations

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 