Probability reseach paper

HEADS TAILS
20 Tosses Observed 13 7
Expected 10 10
Deviation 3 3
30 Tosses Observed 16 14
Expected 15 15
Deviation 1 1
50 Tosses Observed 27 23
Expected 25 25
Deviation 2 2
100 Tosses Observed 56 44
Expected 50 50
Deviation 6 6
Total Observed 112 88
Expected 100 100
Deviation 12 12
  1. In Part 1, what was the expected ratio of heads to tails for tosses of a single coin? Did your results always agree with the expected ratio? If not, what would be a reason for the deviation?
  1. Compare the deviations from the expected for 20, 30, 50 and 100 tosses. What seems to be the relationship between the sample size and deviation?
COMBINATIONS OBSERVED % EXPECTED % DEVIATION
Heads – Heads 12 30% 10 25% 2
Heads – Tails or Tails – Heads 19 47.50% 20 50% 1
Tails – Tails 9 22.50% 10 25% 1
Total 40 100% 40 100% 0
  1. In Part II, what was the probability that tails would appear on both coins? How did you arrive at this answer?
  2. What was the probability that heads-tails (or tails-heads) would appear? Show your calculations. (Hint: The probability for these two combinations must be added together because they were recorded together.)
  3. If you tossed two coins simultaneously 400 times, would you expect the deviation to be greater or less than it was tossing them 40 times?
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