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activity+4 - Activity 4 Surprisingly Predictable The...

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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 (non-consecutive) 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‘ c m :3 o- m i- u. a: an 5 o > < Cluster Size (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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