NIMCET 2016 — Mathematics PYQ

Concept:
we know that,

$P(A)+|P(B)=P(A\cup B)+P(A\cap B)$
$P(A^{\prime })=1-P(A)$

Calculations:

Given, For any two events A and B, the probability that at least one of them occur is 0.6
$\Rightarrow P(A\cup B)=0.6$

and A and B occur simultaneously with a probability 0.3

$\Rightarrow P(A\cap B)=0.3$

we know that,

$P(A)+P(B)=P(A\cup B)+P(A\cap B)$

$\Rightarrow P(A)+P(B)=0.6+0.3=0.9$

Also, we know that

$P(A^{\prime })+P(B^{\prime })=1-P(A)+1-P(B)$

$\Rightarrow P(A^{\prime })+P(B^{\prime })=2-0.9$

$\Rightarrow P(A^{\prime })+P(B^{\prime })=1.1$

Hence, For any two events A and B, the probability that at least one of them occur is 0.6. If A and B occur simultaneously with a probability 0.3, then P(A') + P(B') is 1.1