Question

Of a total of 600 bolts, 20% are too large and 10% are too small. The remainder 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

Answer: (B)

Given total number of bolts = 600 Number of large bolts = 20% of 600 $=\frac{20}{100}\times 600=120$ Number of small bolts = 10% of 600 $=\frac{10}{100}\times 600=60$ $\therefore$ Number of suitable bolts $=600-120-60=420$ $\therefore$ Probability of selecting suitable bolt $=\frac{420}{600}=\frac{7}{10}$ Alternative Method Given total number of bolts = 600 Number of larger bolts = 20% of 600 $=\frac{20}{100}\times 600=120$ $\therefore$ Probability of selecting large bolt $=\frac{120}{600}$ ?.(i) Number of small bolts = 10% of 600 $=\frac{10}{100}\times 600=60$ $\therefore$ Probability of selecting small bolts $=\frac{60}{600}$ ?. (ii) $\therefore$ Probability of getting suitable bolt $=1-\left(\frac{120}{600}+\frac{60}{600}\right)$ $=\frac{600-120-60}{600}=\frac{420}{600}=\frac{7}{10}$