A box contains 10 good articles and 6 with defects. One item is d… - Vidyadip

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:

$\frac{64}{64}$
$\frac{49}{64}$
$\frac{40}{64}$
$\frac{24}{64}$

✓

Answer

$\frac{64}{64}$

Solution:

Let A be the event of drawing one good article whereas B be the event of drawing one defected article.

Here,

$\text{P(A)}=\frac{10}{10+6}=\frac{10}{16}$

$\text{P(B)}=\frac{6}{10+6}=\frac{6}{16}$

The events A and B are mutually exclusive. Thus, the required probability,

$\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}$

$\Rightarrow\text{P}(\text{A}\cup\text{B})=\frac{10}{16}+\frac{6}{16}=\frac{16}{16}=1$

Hence, the correct option is (a).

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