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

Question

Philoid · Accepted Answer

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.