# 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) 64/64 (B) 49/64 (C) 40/64 (D) 24/64 - Mathematics

MCQ

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

•  64/64

•  49/64

•  40/64

• 24/64

#### Solution

$\frac{64}{64}$

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

Here,

$P\left( A \right) = \frac{10}{10 + 6} = \frac{10}{16} \text{ and } P\left( B \right) = \frac{6}{10 + 6} = \frac{6}{16}$
The events A and B are mutually exclusive. Thus, the required probability is $P\left( A \cup B \right) = P\left( A \right) + P\left( B \right)$
$\Rightarrow P\left( A \cup B \right) = \frac{10}{16} + \frac{6}{16} = \frac{16}{16} = 1$

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 29 | Page 73