Answer
a) $\frac{1}{10,000,000,000,000,000}$
b)$\frac{1}{1,000,000,000,000}$
c) $\frac{1}{100,000,000}$
Work Step by Step
a)By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot... \cdot 10=10^{16}=10,000,000,000,000,000.$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{10,000,000,000,000,000}$.
b) By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot... \cdot 10=10^{12}=1,000,000,000,000.$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{1,000,000,000,000}$.
c)By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot... \cdot 10=10^{8}=100,000,000.$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{100,000,000}$.
