A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is
As total articles(nuts + nails) = 10 + 6 = 16
Number of rusted nails = 3
Number of rusted nuts = 5
Number of rusted articles = 8
Let N denotes the event that the article drawn is a nails and R be the event denoting drawn article is rusted
P(N) = 6/16
And P(R) = 8/16
Also, we have possibility that drawn nail is rusted.
∴ P(N ∩ R) = 3/16
P(Nail or Rusted) = P(N ∪ R) = P(N) + P(R) – P(N ∩ R) = 6/16 + 8/16 – 3/16 = 11/16
∴ option (c) is the only correct choice.