Question

A lot of $20$ bulbs contain $4$ defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? Suppose the bulb drawn in is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?

Answer 1

i) $P($Defective bulb$)=\frac{\text{Defective Bulbs}}{\text{Total Bulbs}}=\frac{4}{20}=\frac{1}{5}$

ii) Since one bulb is already drawn, the number of bulbs remaining is $19.$

Number of non defective bulbs is $15$ as one bulb is picked.

$P($Non-defective$)=\frac{15}{19}.$