An online psychic (psi) ability or extrasensory perception (ESP) test shows the participant five face-down cards on the screen and asks the participant to "click on the one card that has a picture on the other side." After clicking a card, the test shows you the card to determine if your guess was correct.
-The ESP test website states: "Keep in mind that your results should only be considered suggestive, because high scores in these tests can be due to chance as well as to actual abilities. Only repeated testing can distinguish between luck and genuine psi abilities." Suppose you take the test five times. How would you simulate the probability of choosing the correct card in at least three of the trials, assuming you do not have ESP?
A) Flip a coin five times and count the number of heads that appear. Repeat this many times. Calculate the proportion of your simulated results that gave 3 or more heads.
B) Spin a spinner five times, where 1/5th of the spinner is red and 4/5ths are white. Record the number of times the spinner lands on white. Repeat this many times. Calculate the proportion of your simulated results where the spinner landed on white at least three times.
C) Take five cards where one card is black and the other four are white. Shuffle the cards and choose five cards with replacement. Record the number of black cards chosen. Repeat this many times. Calculate the proportion of your simulated results where you chose least three black cards.
Correct Answer:
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