Answer
a) $\frac{1}{4}$.
b)$\frac{3}{16}$
c) We can never be absolutely sure.
Work Step by Step
a) The card can be inserted upside down or up and also beginning of the name first or ending of the name first. Hence, by using the fundamental counting rule we can get the number of possibilities: $2\cdot 2=4.$ We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{4}$.
b) P(second try will be correct)=$(1-P(first \ try\ incorrect))\cdot P(second \ try \ correct)=(1-\frac{1}{4})\cdot \frac{1}{4}=\frac{3}{16}$
c) We can never be absolutely sure because it is always possible that we insert the card in an incorrect way, however if we try it more times, it increases are probability.
