$12$ defective pens are accidentally mixed with $132$ good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Five cards - the ten,jack,queen,king and ace of diamonds,are well-shuffled with their face downwards. One card is then picked up at random.
$(i)$ What is the probability that the card is the queen?
$(ii)$ If the queen is drawn and put aside,what is the probability that the second card picked up is $(a)$ an $ace?$ $(b)$ a $queen?$

Which of the following cannot be the probability of an event?

Complete the following statements:
$(i)$ Probability of an event $E +$ Probability of the event 'not $E$' $= \dots \dots \dots \dots \dots$
$(ii)$ The probability of an event that cannot happen is $\dots \dots \dots$. Such an event is called $\dots \dots \dots \dots \dots$
$(iii)$ The probability of an event that is certain to happen is $\dots \dots \dots$. Such an event is called $\dots \dots \dots \dots \dots$

$A$ bag contains $3$ red balls and $5$ black balls. $A$ ball is drawn at random from the bag. What is the probability that the ball drawn is
$(i)$ red?
$(ii)$ not red?

$A$ missing helicopter is reported to have crashed somewhere in the rectangular region shown in the figure. What is the probability that it crashed inside the lake shown in the figure?