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The expected number of heads in 100 tosses of an unbiased coin is?
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The expected number of heads in 100 tosses of an unbiased coin is?
Expected Number of Heads in 100 Tosses of an Unbiased Coin
Introduction
Before we dive into the calculation of the expected number of heads in 100 tosses of an unbiased coin, let us first understand a few basic concepts.
What is an Unbiased Coin?
An unbiased coin is a coin that has an equal probability of landing on either heads or tails. This means that the probability of getting heads and tails is 0.5 or 50% each.
What is Expected Value?
The expected value is the sum of the probability of each possible outcome multiplied by its respective value. In simpler terms, it is the average value that we expect to get from a random event.
Calculation of the Expected Number of Heads in 100 Tosses
Now that we have a basic understanding of the concepts involved, let us move on to the calculation of the expected number of heads in 100 tosses of an unbiased coin.
The probability of getting heads in a single toss of an unbiased coin is 0.5 or 50%.
Since each toss is an independent event, the probability of getting heads in two tosses is:
0.5 x 0.5 = 0.25 or 25%
Similarly, the probability of getting heads in three tosses is:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
By continuing this process, we can calculate the probability of getting heads in 100 tosses as:
0.5 x 0.5 x 0.5 x ... (100 times) = 0.5^100 = 7.8886091 × 10^-31
Therefore, the expected number of heads in 100 tosses of an unbiased coin is:
Expected value = Probability of getting heads x Number of tosses = 0.5 x 100 = 50
Conclusion
In conclusion, the expected number of heads in 100 tosses of an unbiased coin is 50. This means that if we were to toss a coin 100 times, we would expect to get 50 heads and 50 tails, on average.
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The expected number of heads in 100 tosses of an unbiased coin is?
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The expected number of heads in 100 tosses of an unbiased coin is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The expected number of heads in 100 tosses of an unbiased coin is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The expected number of heads in 100 tosses of an unbiased coin is?.
The expected number of heads in 100 tosses of an unbiased coin is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The expected number of heads in 100 tosses of an unbiased coin is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The expected number of heads in 100 tosses of an unbiased coin is?.
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