Question

$\left(i\right)$ A lot of $20$ bulbs contains $4$ defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
$\left(ii\right)$ Suppose the bulb drawn in $\left(i\right)$ 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?

• A. $\left(i\right)\frac{1}{5}\left(ii\right)\frac{15}{19}$
• B. $\left(i\right)\frac{1}{7}\left(ii\right)\frac{19}{23}$
• C. $\left(i\right)\frac{1}{5}\left(ii\right)\frac{12}{23}$
• D. None of these
  

Answer 1

The correct option is A $\left(i\right)\frac{1}{5}\left(ii\right)\frac{15}{19}$

$\left(i\right)$ Total Number of bulbs $=20$
Defective bulbs $=4$
$\therefore$ favorable outcomes $=4$
$\therefore$ probability $=\frac{4}{20}=\frac{1}{5}$
$\left(ii\right)$ Now one non defective bulb is drawn and not replaced.
$\therefore$ Total Number of bulbs $=19$
no. of non defective bulbs are $=15$
$\therefore$ favorable outcomes $=15$
$\therefore$ probability $=\frac{15}{19}$