Question

A box has 14 camera of which 6 are refurbished and 8 are new. If four of these 14 cameras are selected at random without replacement, what is the probability that (i) one new camera will be selected? (ii) at most random without replacement, what is the probability that (i) one new camera will be selected? (ii) at most one new camera will be selected?

Answer 1

Given that, A box has 14 camera of which 6 are refurbished and 8 are new. If four of these 14 cameras are selected at random without replacement.

4 cameras can be selected from 14 by, ¹⁴C₄ = 1001 ways

i) 1 camera can be selected from 8 new cameras by, ⁸C₁ = 8 ways

and other 3 cameras can be selected from 6 refurbished cameras by, ⁶C₃ = 20 ways

Therefore, the probability that one new camera will be selected = 8 * 20 / 1001 = 160 / 1001 = 0.1598

=> probability is 0.1598

ii) At most one camera can be selected by,

[ ⁸C₀ * ⁶C₄ ] + [ ⁸C₁ + ⁶C₃ ] = [ 1 * 15 ] + [ 8 * 20 ] = 15 + 160 = 175 ways

Therefore, the probability that at most one new camera will be selected = 175 / 1001 = 0.1748

=> probability is 0.1748