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One way to solve a probability problem is to repeat the experiment many times, keeping track of the results. Then the probability can be approximated using the basic definition of the probability of an event E: P(E) = n(E)/n(S), where E occurs n(E) times out of n(S) trials of an experiment. This is called the Monte Carlo method of finding probabilities. If physically repeating the experiment is too tedious, it may be simulated using a random-number generator, available on most computers and scientific or graphing calculators. To simulate a coin toss or the roll of a die on the TI-84 Plus C, change the setting to display 0 digits, and enter rand or rand * 6+.5, respectively. For a coin toss, interpret 0 as a head and 1 as a tail. In either case, the ENTER key can be pressed repeatedly to perform multiple simulations.
Suppose a coin is tossed 5 limes. Use the Monte Carlo method with at least 50 repetitions to approximate the following probabilities.
(a) P(exactly 4 heads) (b) P(2 heads and 3 tails)
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Finite Mathematics (11th Edition)
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