Question

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

(a) > 0.5 (b) 0.5 (c) ≤ 0.5 (d) 0

Answer 1

$$\begin{gathered} \mathrm{Given};P\left(\overline{A}\right)=0.2 \\ P\left(\overline{B}\right)=0.3 \\ \therefore P\left(A\right)=1-P\left(\overline{A}\right)=0.8\mathrm{and}\left(B\right)=1-P\left(\overline{B}\right) \\ P\left(B\right)=0.7 \\ \therefore \mathrm{Required}\mathrm{Probability}=P\left(\overline{A}B\right)+P\left(A\overline{B}\right) \\ =0.2\times 0.7+0.8\times 0.3 \\ =0.38\le 0.5 \end{gathered}$$
Hence, the required answer option C.