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:

$p_1=100\cdot \frac{3}{12}=\frac{100\cdot 3}{12}=\frac{300}{12}=25\%$

$p_2=100\cdot \frac{3}{12}=\frac{100\cdot 3}{12}=\frac{300}{12}=25\%$

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

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