Question

Of a total of $600$ bolts, $20\%$ are too large and $10\%$ are too small. The remaining are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable is

• A. $\frac{1}{5}$
• B. $\frac{7}{10}$
• C. $\frac{1}{10}$
• D. $\frac{3}{10}$

Answer 1

The correct option is B

$\frac{7}{10}$

Explanation for the correct option(s)

Find the probability

Let the too large number of bolts can be expressed as,

$\Rightarrow \frac{600\times 20}{100}=120$

And the too small number of bolts can be expressed as,

$\Rightarrow \frac{600\times 10}{100}=60$

Total bolts can be expressed as,

$\Rightarrow 120+60=180$

Then the number of suitable bolts can be expressed as,

$\Rightarrow 600-180=420$

Then find the probability of suitable bolts

$\Rightarrow P=\frac{F}{T}$

Here, $P$ is the probability, $F$ is the number of favorable bolts, and $T$ is the total bolts.

$$\begin{gathered} P=\frac{420}{600} \\ =\frac{7}{10} \end{gathered}$$

Hence, option B is correct .