A student creates a simulation that “flips a coin” 200 times in a row (randomly

Question

A student creates a simulation that “flips a coin” 200 times in a row (randomly generates 0’s and 1’s), recording whether or not there is a sequence of six 0’s or six 1’s. The student runs this simulation 1000 times (therefore "flipping a coin" a total of 200,000 times). In 785 of the trials the student finds a sequence of at least six 0's or six 1's. The student then reports that the probability of getting six heads or six tails in a row when flipping a coin 200 times is precisely 0.785. What is wrong with this statement? HINT - There is not an error in the calculation of 0.785 as the probability. The theoretical probability of getting 6 heads or 6 tails in a row is very close to that.

Explanation / Answer

Simulation has been created by the student that flips a coin 200 times in a row. When simulation is done 1000 times which means total of 200000 times a coin is flipped and in 785 of the trials the student finds a sequence of at least six 0's or six 1's. That means 0.785 is the parameter value and not probability value although the probabilty of getting six 0's or 1's might be close to 0.785 which signifies the parameter estimate of flipping a coin 200 times in a row.

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