Let $$\mathrm{A}$$ and $${B}$$ be two events such that $$P(A / B)=\frac{1}{2}$$ and $$P(B / A)=\frac{1}{3}$$ and $$P(A \cap B)=\frac{1}{6}$$ then, which one of the following is not true?

A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

Suppose we have three cards identical in form except that both sides of the first card are coloured red, both sides of the second are coloured black, and one side of the third card is coloured red and the other side is coloured black. The three cards are mixed and a card is picked randomly. If the upper side of the chosen card is coloured red, what is the probability that the other side is coloured black.

What is the probability of a randomly chosen 2 digit number being divisible by 3 ?