The big clock

The big clock hands stopped at a random moment. What is the probability that:

a) a small hand showed the time between 1:00 and 3:00?
b) the big hand was in the same area as a small hand in the role of a)?
c) did the hours just show the time between 21:00 and 22:30?

Correct answer:

p₁ =  25 %
p₂ =  25 %
p₃ =  12.5 %

Step-by-step explanation:

$p_1=100\cdot {\displaystyle \frac{3}{12}}=25\mathrm{\%}$

$p_2=100\cdot {\displaystyle \frac{3}{12}}=25\mathrm{\%}$

$p_3=100\cdot {\displaystyle \frac{22.50-21.00}{12}}={\displaystyle \frac{25}{2}}\mathrm{\%}=12.5\mathrm{\%}$

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