The definition of uniform distribution can be found on the website, for example. The figure shows the image and the definition of constant distribution taken from site https://mathworld.wolfram.com/UniformDistribution.html .
Answers:
a) In our case "a=3; b=21 min" , respectively the probability density function "P(X)=\\frac{1}{18}" ;
b) The probability that Kate will be no more than 10 minutes late "P_b" is the area under the curve "P(X)" from the value "X=a" to the set value of "X=10 min".Thus, "P_b=\\frac{(10-3)}{18}=\\frac{7}{18}" ;
c) Similarly "P_c=\\frac{20-15}{18}=\\frac{5}{18}" ;
d) The probability that Kate will be exactly "X=12 min" late equals "P_d=P(X)=0" .
e) If everything goes without delays, you and Katya will be seated in the cinema at time T=7:25+0:21+0:07=7:53. Before the start of the session, you could have 7 minutes, but Katya is usually at least 3 minutes late, so your margin is 4 minutes, and the probability of being in time is "P_e=\\frac{4}{18}=\\frac{2}{9}" .
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