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Math 116 – Introduction to Chapter 4 Due next class (2, 3-a,b,c) Name_________________ 1) Consider the experiment of “tossing a coin three times and counting the number of heads”. (a) Develop the sample space of the experiment by using a tree diagram (b) Construct a frequency distribution. (c) Construct a frequency histogram. (d) Construct a probability distribution. (e) Construct a probability histogram. (f) If we toss a coin three times, what is the “theoretical” probability of getting exactly 2 heads? (g) Find P(x 2) 2) Simulation *** Now we’ll simulate the experiment of “tossing a coin three times” and counting the number of heads”. Let 1 = Head 2 = Tail Use your calculator to generate three random integers from 1 to 2 by doing MATH PRB 5:randInt(1,2,3) ENTER (this is one repetition of the experiment) Repeat the experiment 25 times and record information in the table. (keep pressing ENTER 24 more times and tally results below) #head s 0 1 2 3 tally frequenc y (a) If we toss a coin three times, what is the “experimental” probability of getting exactly 2 heads? (compare with (f) in previous page) (b) Find P(x 2) (compare with (g) in previous page) Law of Large Numbers As we repeat an experiment a large number of times, the “experimental” probability gets closer to the “theoretical” probability. 3) Consider the experiment of “having four children and counting the number of girls” a) Develop the sample space of the experiment by using a tree diagram b) Construct a frequency distribution. c) Construct a frequency histogram. d) Construct a probability distribution e) Construct a probability histogram f) What is the “theoretical” probability of having exactly 3 girls? g) Find P(x 3) h) Simulate the experiment repeating 20 times i) Answer (f) and (g) again to find the “experimental” probabilities and compare answers.