Question

The probability that at least one of the events A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then P(A) + P(B)=
(a) 0.4
(b) 0.8
(c) 1.2
(d) 1.6

Answer 1

The probability that at least one of the events A and B occur is 0.6
i.e $P\left(A\cup B\right)=0.6$
and probability that A and B occur simultaneously is 0.2
$$\begin{gathered} \mathrm{i}.\mathrm{e}.P\left(A\cap B\right)=0.2 \\ \mathrm{Since}P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ \mathrm{i}.\mathrm{e}.0.6=P\left(A\right)+P\left(B\right)-0.2 \\ \mathrm{i}.\mathrm{e}.P\left(A\right)+P\left(B\right)=0.8 \\ \mathrm{i}.\mathrm{e}.1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)=0.8 \\ \mathrm{i}.\mathrm{e}.P\left(\overline{A}\right)+P\left(\overline{B}\right)=2-0.8 \\ \mathrm{i}.\mathrm{e}.P\left(\overline{A}\right)+P\left(\overline{B}\right)=1.2 \end{gathered}$$
Hence, the correct answer is option C.