Math Quiz: Math for - The random and time modules

1. A lottery machine contains balls numbered from 1 to 50 inclusive. If one ball is drawn at random, what is the probability that the number on the ball is a multiple of 7?

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2. A process selects an integer uniformly at random from the set \(\{10, 11, 12, \dots, 25\}\). How many distinct integers can be selected?

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3. An experiment starts at 09:45:30 and ends at 10:02:15 on the same day. What is the total duration of the experiment in seconds?

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4. If a random integer \(N\) is generated such that \(5 \le N < 15\), what is the sum of the smallest and largest possible values of \(N\)?

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5. A sensor generates a data point every 0.5 seconds. The first data point is generated at time \(t=0\) seconds.

   1. If the sensor operates for exactly 60 seconds, how many data points are generated in total?

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   2. What if the sensor's generation interval is changed to 0.2 seconds, still operating for 60 seconds, with the first point at \(t=0\)? How many data points would be generated then?

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