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??
pl explain step by step properly..

Dear Student,
Please follow the solution to the above given query:
Number of bolts in the box = 100
Number of nuts in the box = 50
Number of bolts that are rusted = 50
Number of nuts that are rusted = 25
Total number of items in the box = 100 + 50 = 1500
Total number of rusted items = 50 + 25 = 75
Number of ways of drawing 2 items out of 150 = 150C2
Total number of elementary events = 150C2
Consider the following events :A = 2 items drawn are rusted; B = 2 items drawn are bolts
Now, there are 75 rusted items out of which 2 can be drawn in 75C2 ways.
So, P(A) = C275C2150=277511175
There are 100 bolts in the box, out of which 2 can be drawn in 100C2 ways.
So, P(B) = 1002C2150=495011175
There are 50 bolts that are rusted, out of which 2 can be drawn in 50C2 ways.
P(AB) = C250C2150=122511175
Required probability = P(AB) = P(A) + P(B)  P(AB) = 277511175+495011175-12251175=7725-122511175=650011175=260447answer 
Hope this information will clear your doubts about Probability.

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