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} $