What does the law of large numbers (Bernoulli) predict will be the percentage of heads if you flip a coin many times.(a) If you flip a coin 500 times, about how many heads would you predict?(b) Flip a coin 100 times. How many heads did you get? What is the percentage of heads? (c) Flip the coin 100 more times. How many heads did you get? What is your percentage of heads for the 200 flips? (d) Flip the coin 300 more times. What is the percentage of heads for all 500 flips? Is this more or less than is expected?

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Asked Dec 13, 2019
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What does the law of large numbers (Bernoulli) predict will be the percentage of heads if you flip a coin many times.


(a) If you flip a coin 500 times, about how many heads would you predict?
(b) Flip a coin 100 times. How many heads did you get? What is the percentage of heads? 
(c) Flip the coin 100 more times. How many heads did you get? What is your percentage of heads for the 200 flips?
(d) Flip the coin 300 more times. What is the percentage of heads for all 500 flips? Is this more or less than is expected?

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Expert Answer

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Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case you require the unanswered parts also, kindly re-post that parts separately.

Step 2

(a)

 

The predicted number of heads when a coin is flipped 500 times is 250 and it is calculated below:

 

When tossing a coin, the outcomes are head and tail. The probability of getting head is p=0.5 and the probability of getting tail is (1-p)=0.5. The sample size(n) is 500.

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Predicted number of heads = np = 500 x 0.5 = 250

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Step 3

(b)

 

The predicted number of heads when a coin is flipped 100 times...

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Predicted number of heads = np =100 x0.5 = 50

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