Question

A box contains 24 light bulbs, of which two are de- fective. If a person selects 10 bulbs at random, without replacement, what is the probability that both defective bulbs will be selected?

Answer 1

Total light bulbs = 24

Defective bulbs = 2

Non defective bulbs = 22

The probability of selecting 10 bulbs with two defective bulbs

We will use combination formula which states:

`^nC_r = (n!)/(r!(n-r)!)`

=
`(^2C_2 * ^(22)C_8)/(^(24)C_(10))`

=
`(10 * 9)/(24 * 23)`

=
`(90)/(552)`

= 0.16

Therefore, the probability that both defective bulbs will be selected is 0.16