Example 1Example 1We’ll do two together:iClickerExample 1Find the PROBABILITY of getting a run of at least 3 consecutive “heads” or run of at least 3 consecutive “tails” in the experiment where fair coin is tossed 10 times•Step 1 Give a probability model•Each toss has a probability 0.5 of “heads” and 0.5 of “tails”•Tosses are independent of one another (recall: independence – outcome of one toss of the coin does not change the probability of the outcome of any other toss)Example 1•Step 2 Assign digits to represent outcomes•Goal: assign digits in a way that matches the probabilities from Step 1•Solution: (one of several possibilities) •Use Table of Random Digits (Table A in text)•Let one digit represent 1 toss of the coin–Odd digit represents heads–Even digit represents tails•Rationale: –Works because each digit in the table has a 1/10 chance to be the next digit and successive digits are independent, so 5/10 = half the digits are odd and 5/10 = half the digits are even •Step 3 Simulate many repetitionsWe’ll do two together:Line 101: 19223 95034 05756 28713 96409 12531 42544 82858Line 121: 71487 09984 29077 14863 61683 47052 62224 51025Line 140: 12975 13258 13048 45144 72321 81940 00360 02428Line 150: 07511 88915 41267 16853 84569 79367 32337 03316•Odd digit represents heads / Even digit represents tails•48 45144 723 THTTTHHTT HNow you do one!•Choose a starting point•Choose a string of 10 consecutive digits•Assign H or T to each digit using rule:“Odd digit represents heads / Even digit represents tails”•Determine whether you have a string of 3 heads or 3 tails•YES, we have a string of 3 tails•32337 03316 H T H H H T H H H T YES, string of 3 (2 actually)iClickerUse your iClicker to record whether you had a run of at least three “heads” or at least three “tails” in your one repetition.•Did you have a run of at least 3 “heads” or at least 3 “tails”A. YESB. NOSo, our estimate of the probability of getting a run of at least 3 “heads” or at least 3 “tails” our of 10 coin flips is:•for Section 002, the proportion of responders with runs of at least 3 “H” or “T” was: 127/158 = 0.837•for Section 003, the proportion was (couldn’t find notes…)less than 0.75In the text (pp. 441-442), they describe their experiment using 25 repetitions. In 23 of them, they had a run of 3 or more heads or tails. Their estimated probability was P(run of at least 3 heads or tails) = 23 / 25 =
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