Unformatted text preview: Activity 4  Surprisingly Predictable The probability of getting heads or tails on a fair toss are exactly equal. So we can write the
probability of heads or tails as 1/2 (or 0.5). The probability of getting two heads in a row is 1/2 x 1/2 =
1/4 [or 0.25). The probability of getting three heads in a row is 1/2 x 1/2 x 1/2 = '/a and so on. Using
these rules, mathematicians can calculate the expected frequency of any series of consecutive
results. The expected frequencies results for 100 coin flips are provided in Table 5 below. Table 5  Expected Cluster Frequencies for 100 Coin Flips m—nnnunnnun
mmamnmmmmmmm This table tells you that if you flip a coin 100 times, you should expect to see 25 single (nonconsecutive)
results. You should also expect 12.5 pairs of consecutive heads or tails, 6.25 triples etc. Remember that real clusters are counted in whole numbers (integers) but their average frequency can be a
fraction. Step 1  Comparing your results Plot your results from the Average column in Table 3 on the graph below. Use the blank space to the
right ofeach grey bar for each cluster size. 5‘
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(Number of consecutive heads and consecutive tails} How closely did the average results of your combined results (representing 1000 coin flips) match the
expected average frequencies of each cluster size? ...
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 Fall '08
 Feldman

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