Question

A box contains twenty-five screws which are identical in size, but 13 of which are copper coated and 12 of which are not. Two screws are selected at random, without replacement.

(a) Find the probability that both are copper coated.
(b) Find the probability that at least one is copper coated.

Answer 1

Answer:

Total number of screws = 25

Screws coated with copper = 13

Without replacement = 2

Not coated = 12

a)

To give the probability that both are copper coated

i.e.,

= 13C2*12C0 / 25C2

= 78*1 / 300

= 0.26

b)

To determine the probability that at least one is copper coated

= P(X >= 1)

= 1 - P(X < 1)

= 1 - P(x = 0)

= 1 - [13C0*12C2 / 25C2]

= 1 - [1*78 / 300]

= 1 - 0.26

= 0.74