Problem

What is the probability of obtaining seven heads in a row when flipping a coin? Interpret this probability.
Interpret this probability.
Consider the event of a coin being flipped seven times. If that event is repeated ten thousand different times, it is expected that the event would result in seven heads about $\square$ time(s).
(Round to the nearest whole number as needed.)

Answer

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Answer

Final Answer: It is expected that the event would result in seven heads about \(\boxed{78}\) times.

Steps

Step 1 :The probability of getting a head in a single coin flip is \(\frac{1}{2}\).

Step 2 :Since the coin flips are independent events, the probability of getting seven heads in a row is \(\left(\frac{1}{2}\right)^7\).

Step 3 :To find out how many times this event would occur in ten thousand trials, we multiply the probability by the number of trials.

Step 4 :\(prob_{head} = 0.5\)

Step 5 :\(num_{flips} = 7\)

Step 6 :\(num_{trials} = 10000\)

Step 7 :\(prob_{sevenheads} = 0.0078125\)

Step 8 :\(expected_{occurrences} = 78.125\)

Step 9 :Round \(expected_{occurrences}\) to the nearest whole number, we get 78.

Step 10 :Final Answer: It is expected that the event would result in seven heads about \(\boxed{78}\) times.

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