Validity of a proposed discrete distribution, an unknown constant in a second and probabilities from a distribution given by a formula

A game uses three bags of discs, \(A\), \(B\) and \(C\). Every disc shows one of the numbers \(1\), \(2\), \(5\) or \(7\). Let \(X\) be the number on a disc taken at random from a bag.

1. The table below was suggested as the probability distribution of \(X\) for bag \(A\). Explain why it cannot be a probability distribution.[2]

   \(x\)	\(1\)	\(2\)	\(5\)	\(7\)
   \(\mathrm{P}(X=x)\)	\(0.2\)	\(0.35\)	\(0.15\)	\(0.2\)

2. For bag \(B\), the probability distribution of \(X\) is shown below, where \(k\) is a constant. Find the value of \(k\).[2]

   \(x\)	\(1\)	\(2\)	\(5\)	\(7\)
   \(\mathrm{P}(X=x)\)	\(0.3\)	\(k\)	\(3k\)	\(0.1\)

3. For bag \(C\), the probability distribution of \(X\) is given by \(\mathrm{P}(X=x)=\dfrac{x+1}{19}\), for \(x=1,\ 2,\ 5,\ 7\). One disc is taken at random from bag \(C\).
   1. Find the probability that the number on the disc is \(5\).
   2. Find the probability that the number on the disc is less than \(5\).[4]