$A$ 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.

Two customers,Shyam and Ekta,are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on
$(i)$ the same day?
$(ii)$ consecutive days?
$(iii)$ different days?

It is given that in a group of $3$ students,the probability of $2$ students not having the same birthday is $0.992$. What is the probability that the $2$ students have the same birthday?

Two dice,one blue and one grey,are thrown at the same time.
$(i)$ Complete the following table:
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Sum} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text{Prob.} & \frac{1}{36} & & & & & & \frac{5}{36} & & & & \frac{1}{36} \\ \hline \end{array}$
$(ii)$ $A$ student argues that 'there are $11$ possible outcomes $2, 3, 4, 5, 6, 7, 8, 9, 10, 11$ and $12$. Therefore,each of them has a probability $\frac{1}{11}$.' Do you agree with this argument? Justify your answer.

$A$ bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
$(i)$ an orange flavoured candy?
$(ii)$ a lemon flavoured candy?

$A$ box contains $12$ balls out of which $x$ are black. If one ball is drawn at random from the box,what is the probability that it will be a black ball?
If $6$ more black balls are put in the box,the probability of drawing a black ball is now double of what it was before. Find $x$.