# 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?

Toolbox:
• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Step 1:
Given probability of first examination P(I)=0.8
P(II)=0.7
Probability of atleast (I or II)=$P(I \cup II)=0.95$
$\therefore P(I \cup II)=P(I)+P(II)-P(I \cap II)$
$0.95=0.8+0.7-P(I \cap II)$
Step 2:
$\therefore P(I \cap II)=1.5-0.95$
$\Rightarrow 0.55$
$\therefore$ Probability of passing both is 0.55
Hence (A) is the correct answer.