Question

A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
(a) $\frac{64}{64}$

(b) $\frac{49}{64}$

(c) $\frac{40}{64}$

(d) $\frac{24}{64}$

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\frac{64}{64} \\ \mathrm{P}\left(\text{good item}\right)=\frac{10}{16} \\ \mathrm{P}\left(\text{defected item}\right)=\frac{6}{16} \\ \mathrm{P}\left(\text{either good or defected item}\right)=\mathrm{P}\left(\text{good item}\right)+\mathrm{P}\left(\text{defected item}\right) \\ =\frac{10}{16}+\frac{6}{16} \\ =\frac{16}{16} \\ =1 \\ =\frac{64}{64} \end{gathered}$$