How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads?

Final answer:

In a series of 50 coin tosses, a coin needs to land heads 30 times to have an experimental probability 20% greater than the theoretical probability.

Explanation:

The subject of focus here is the allusion to the theory of probability, particularly in relation to a fair coin flip. The theoretical probability of obtaining either heads or tails in a coin flip is 0.5. However, the student is interested in having an experimental probability 20% greater than the theoretical probability.

We can first calculate the theoretical counts of expected heads per 50 tosses, which is (0.5 * 50) = 25. This result represents the notion that if a coin is thrown 50 times, on average, will land heads 25 times based on the theoretical probability.

To achieve an experimental probability 20% greater than the theoretical probability, we need to find a count of heads that corresponds to a probability that is 20% more than 0.5 (the theoretical probability). This new probability is therefore 0.6 and the corresponding count of heads required would be (0.6 * 50) = 30. Hence, in 50 tosses, the coin would need to show heads 30 times to have an experimental probability 20% greater than the theoretical probability of getting heads.

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