Question

Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective? 

Hint:

When selecting without replacement, always use combinations. Favorable outcomes over total outcomes gives the probability.

Answer 1

Step 1: Total number of bulbs. 
There are 20 bulbs in total, of which 2 are defective and 18 are good. 
Step 2: Number of ways to choose 2 bulbs. 
Total ways: \[ \binom{20}{2} = \frac{20 \times 19}{2} = 190. \] Step 3: Favorable outcomes. 
Choose 2 good bulbs from 18: \[ \binom{18}{2} = \frac{18 \times 17}{2} = 153. \] Step 4: Probability. 
\[ P(\text{no defective}) = \frac{\binom{18}{2}}{\binom{20}{2}} = \frac{153}{190}. \] Step 5: Conclusion. 
Thus, the probability is: \[ \boxed{\frac{153}{190}} \]