Question

A Box contains 50 Bolts and 50 nuts. Half of the Bolts and nuts are rusted. if two item are drawn with replacement, what is the probability that either both rusted or both are bolts. Please Explain step by step

Answer 1

Hello mate!!

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.


Hope it helpful