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
$A)\dfrac{1}{5}$
$B)\dfrac{7}{{10}}$
$C)\dfrac{1}{{10}}$
$D)\dfrac{3}{{10}}$

Answer 1

First, we need to know about the concept of Probability which is the term mathematically with events that occur, which is the number of favorable events that divides the total number of the outcomes.
The concept of Percentage is used to find the share or amount of something in terms of $100$. The percentage formula is given by: Percentage = given value divided by total value $\times 100$

Formula used:
$P = \dfrac{F}{T}$in this formula P is the overall probability, F is the possible favorable events and T is the total outcomes from the given.

Complete step-by-step solution:
Since from the given that we have total bolts are $600$ and hence which is the total outcome.
Since $20\%$ are too large and $10\%$ are too small. Out of the $600$ bolts $20\%$ are too large and that means we have $\dfrac{{20}}{{100}} \times 600 = 120$ bolts are too large and also Out of the $600$ bolts $10\%$ are too small and that means we have $\dfrac{{10}}{{100}} \times 600 = 60$ bolts are too small.
Hence the total number of the larger and smaller bolts are $60 + 120 = 180$ (unsuitable bolts)
Since we know that total bolts are $600$ and we will subtract it with the unsuitable bolts $180$ to get the suitable bolts.
Thus, by the subtraction operation, we get $600 - 180 = 420$ suitable bolts and thus which are the favorable possible events.
Thus, we have total outcome events are $600$ and favorable events are $420$. By the use of probability formula, we get $P = \dfrac{F}{T} \Rightarrow \dfrac{{420}}{{600}}$ and by the division operation we get $P = \dfrac{{420}}{{600}} = \dfrac{7}{{10}}$
Thus, the suitable bolt is selected at random is $\dfrac{7}{{10}}$
Therefore, the option $B)\dfrac{7}{{10}}$ is correct.

Note: Do not take the total not suitable bolts count as $120 - 60$ which is the wrong method, because to find the total unsuitable bolts we only need to add the larger and smaller bolts not to subtract.
If we divide the probability and then multiplied with the hundred then we will determine its percentage value.
Which is $\dfrac{7}{{10}} = 0.7 \times 100 = 70\%$ of the suitable bolts chosen at random
In probability, $\dfrac{1}{6}$ which means the favorable event is $1$ and the total outcome is $6$.