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STA 200 chapter17

STA 200 chapter17 - Chance If you toss a coin repeatedly...

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Chance

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If you toss a coin repeatedly, you might expect it to come up heads half the time. Suppose you toss a coin 10 times. For the coin to come up heads half the time, you would have 5 heads and 5 tails after 10 tosses. Would it seem strange to get 4 heads instead of 5? How about 6 heads? (For that matter, would 3 heads or 7 heads seem out of the ordinary?)
Using a fair coin, the probability of obtaining 5 heads in 10 flips is only about 24.6%. In general, chance behavior is unpredictable in the short run, but it has a regular and predictable pattern in the long run. A phenomenon is random if individual outcomes are uncertain, but there is a regular distribution of outcomes in a large number of repetitions.

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When repeatedly tossing a coin, the proportion of heads will vary quite a bit at first. After more and more tosses, the proportion will get close to 0.5 and stay there. Probability is an idealization based on an extrapolation of what would happen in an infinitely long series of trials.
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STA 200 chapter17 - Chance If you toss a coin repeatedly...

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