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AP® Statistics

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Difficult

Psychic Abilities

APSTAT-AL6VYK

A researcher wants to determine whether a proclaimed psychic really has any special abilities.

Four decks of regular playing cards are shuffled together so that the researcher has $208$ cards in a pile. Half the cards are colored red, and the other half are black. As the researcher looks at each card, the blindfolded psychic calls out the card’s color.

At the $5\%$ level of significance, what is the least number of cards the mind reader must call correctly to show that he is not merely guessing?

A

$55$

B

$104$

C

$108$

D

$112$

E

$116$