Question

A box contains 100 bolt and 50 nuts. if it is given that 50% bolts and 50% nuts are rusted. two objects are selected from the box at random . find the probability that both are bolts or bolts are rusted??\n pl explain step by step properly..

Answer 1

Solution:-
Number of bolts in the box = 100
Number of nuts in the box = 50
Number of rusted bolts = 50
Number of rusted nuts = 25
Total number of items in the box = 100+50 = 150
Total number of rusted items in the box = 50+ 25 = 75
Consider the following events : A = Event of getting a rusted item, B = Event of getting a bolt and A ∩ B = Event of getting a rusted bolt.
Number of ways of drawing 2 items out of 150 = 150c₂
There are 75 rusted items, out of which 2 can be drawn in 75c₂ ways
So, P (A) = 75c₂/150c₂ = (75*74/2*1)/(150*149/2*1)
P (A) = 2775/11175
There are 100 bolts in the box, out of which 2 can be drawn in 100c₂ ways.
So, P (B) = 100c₂/150c₂ = (100*99/2*1)/(150*149/2*1)
P (B) = 4950/11175
There are 50 bolts that are rusted, out of which 2 can be drawn in 50c₂ ways.
P (A ∩ B) = 50c₂/150c₂ = (50*49/2*1)/(150*149/2*1)
P (A ∩ B) = 1225/11175
So, the required probability = P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
= 2775/11175 + 4950/11175 - 1225/11175
= (7725 - 1225)/11175
= 6500/11175
P (A ∪ B) = 260/447
Answer.