A stranger stops you on the street claiming to be a psychic, and strongly insist

Question

A stranger stops you on the street claiming to be a psychic, and strongly insists that you let her read your fortune. To test this, you have a deck of 50 cards that are either black or white on the other side, and ask her to predict the color of each card. She manages to correctly guess 32 cards in total.

(a) Assume that there is no feedback after each guess (i.e. she does not know if each guess is correct.) Determine whether or not this result is meaningful.

(b) Determine the power of this test, assuming that someone with psychic abilities can typically guess correctly 66% of the time.

(c) Consider the situation in which she is given feedback after every guess. Explain how your conclusion from part (a) may be different.

Thanks!

Explanation / Answer

The stranger claims who claims to be a psychic correctly guess 32 out of 50 cards,

thus the probability of correctly answering is= 32/50=0.64, i.e the stranger can guesscorrectly 64% of the time

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