 Hello friends! Let's solve the following question. It says, 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 at least one of them is 0.95. What is the probability of passing both? Let us now move on to the solution and let A be the event of passing. The probability that randomly chosen student passes the first exam is 0.8, so probability of A is 0.8 and probability of B is 0.7. And we are given that the probability of passing at least one of the two examinations is 0.95. That is the probability that student passes in any one of the examinations, at least any one of them examination is 0.95. That is he either passes in first examination or he passes in the second examination. So the probability of A or B which is equal to probability of A union B is given to be 0.95. We have to find the probability of passing in both the examinations that is A and B. Now we know that probability of A or B is equal to probability of A plus probability of B minus probability of A and B. So this implies probability of A and B is equal to probability of A plus probability of B minus probability of A or B. Now probability of A is 0.8, probability of B is 0.7 and probability of A or B is 0.95 which is equal to 1.5 minus 0.95 which is equal to 0.55. Hence the probability of passing in both examinations is 0.55. So this completes the question and the session. Bye for now. Take care. Have a good day.