The big clock

The hands of a clock stop at a random moment. What is the probability that:

a) the hour hand shows a time between 1:00 and 3:00?
b) the minute hand is in the same region as the hour hand as described in part a)?
c) the clock shows a time between 21:00 and 22:30?

Final 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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