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:

$^nC_r = \frac{n!}{r!(n-r)!}$

= $\frac{^2C_2 \times ^{22}C_8}{^{24}C_{10}}$

= $\frac{10 \times 9}{24 \times 23}$

= $\frac{90}{552}$

= 0.16

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