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, then find the probability that it is rusted or is a nail.

Explanation

The total number of nails and nuts is 6 + 10 = 16.
P(R ) = `(1)/(2)` (R stands for rusted)
P(N) = `(6)/(16)` (N stands for nails)
`P(R nn N) = (3)/(16)` [`because` 3 nails are rusted out of 6 nails]
`therefore P(R uu N) = P(R) + P(N) - P(R nn N)`
`=(1)/(2) + (6)/(16) - (3)/(16) = (8 + 6 - 3)/(16) = (11)/(16)`