Question

In an entrance test 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 of them is $$0.95$$. What is the probability of passing both?

Answer 1

Let A and B denote the events that a randomly chosen student passes first and second examinations respectively.

Then,

$$P\left(A\right)=0.8$$

$$ P\left(B\right)=0.7$$

$$P\left(A\cup B\right)=0.95$$

Required probability $$= P\left(A\cap B\right)$$ $$=$$$$ P\left(A\right)+ P\left(B\right)- \left(A\cup B\right)$$

$$=0.8+0.7-0.95=0.55$$