Question

A box contains $10$ good articles and $6$ with defects. One article is chosen at random. What is the probability that its is either good or has a defect.

• A. $\frac{24}{64}$
• B. $\frac{40}{64}$
• C. $\frac{49}{64}$
• D. $\frac{64}{64}$

Answer 1

The correct option is D

$\frac{64}{64}$

Explanation for the correct answer:

Step-1: Probability of individual event:

Number of good articles $=10$

Number of defective articles $=6$

Total number of articles $=16$

The event of choosing a good article $=\frac{10}{16}$

The event of choosing a defective article $=\frac{6}{16}$

Step 2: Finding the probability

Thus the probability of choosing either a good or a defective,

$$\begin{gathered} =\frac{10}{16}+\frac{6}{16} \\ =\frac{16}{16} \\ =1 \end{gathered}$$

From the given options we need to find which fraction is equal to 1. Option$\frac{64}{64}$ is equivalent to $1$.

Hence option (D) is the correct answer.