Jane Doe claims to possess extrasensory perception (ESP). She says she can guess more often than not

Question:

Jane Doe claims to possess extrasensory perception (ESP). She says she can guess more often than not the outcome of a flip of a balanced coin in another room. In an experiment, a coin is flipped three times. If she does not actually have ESP, find the probability of the number of her correct guesses.
a. Do this by constructing a sample space, finding the probability for each point, and using them to construct the probability Do this using the formula for the binomial Distribution
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