A drawer contains 50 bolts and 150 nuts Half of the bolts and half of the nuts are rusted If one ite...........

Quantitative Aptitude ( CCS) Probability

A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a bolt?

3/8

1/2

5/8

None of these

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Explanation:

Sample space = 50 bolts + 150 nuts
= 200
Number of bolts rusted = 25
Number of nuts rusted = 75
Let A be the event of getting an item that it is a rusted item
A = 25 bolts + 75 nuts
n (A) = 100
P (A) = n (A)/n (S)
= 100/200
Let B be the event of getting an item that it is a bolt
n (B) = 50
P (B) = n (B)/n (S)
= 50/200
25 bolts are in both the events A and B
n (A ∩ B) = 25
P (A ∩ B) = n (A ∩ B)/n (S)
= 25/200
the probability that it is rusted or that it is a bolt
P (A U B) = P (A) + P (B) - P (A ∩ B)
= (100/200) + (50/200) - (25/200)
= (100 + 50 - 25)/200
= (150 - 25)
= 125/200
P (A U B) = 5/8