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### “Sixty percent of the time, it works every time” – Brian Fantana, Anchorman In this week’s material, we cover the basics of probability including trials, outcomes, and events. We also consider some simple applications of Monte Carlo simulation. This week’s homework will focus on these topics.Basic probabilityWhich term refers to the set of possible outcomes associated with a trial? Review this week’s math notes on basic probability if necessary.

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### Which Python expressions below simulate a single trial corresponding to the roll of a fair six-sided die whose faces are numbered 1 to 6?

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### What is the expected value of trial(n) as a function of n? (Here, assume that n is a positive integer.) Enter the answer below as a math expression in n. def trial(n): val = random.randrange(n) return valAs a hint, note that the arithmetic sum 0 + 1 + 2 + .. + k0+1+2+..+k has the value \frac{1}{2}k(k+1) 21 k(k+1).

## Q:

### Given a standard deck of 52 cards, what is the probability that two cards drawn at random will have the same rank? Note that first card drawn is not added back into the deck when the second card is drawn.

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