Savita and Hamida are friends. What is the probability that both will have $(i)$ different birthdays? $(ii)$ the same birthday? (ignoring a leap year).

Which of the following arguments are correct and which are not correct? Give reasons for your answer.
$(i)$ If two coins are tossed simultaneously,there are three possible outcomes - two heads,two tails,or one of each. Therefore,for each of these outcomes,the probability is $\frac{1}{3}$.
$(ii)$ If a die is thrown,there are two possible outcomes - an odd number or an even number. Therefore,the probability of getting an odd number is $\frac{1}{2}$.

$(i)$ $A$ 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?
$(ii)$ Suppose the bulb drawn in $(i)$ 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?

$A$ game consists of tossing a one rupee coin $3$ times and noting its outcome each time. Hanif wins if all the tosses give the same result,i.e.,three heads or three tails,and loses otherwise. Calculate the probability that Hanif will lose the game.

Harpreet tosses two different coins simultaneously (say,one is of $Rs. 1$ and other of $Rs. 2$). What is the probability that she gets at least one head?

$A$ bag contains $5$ red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball,determine the number of blue balls in the bag.