A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 6 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 5 of the 6 cups. (a) What are her chances of having her claim granted if she is in fact only guessing? (b) What are her chances of having her claim rejected when in fact she really does have the ability she claims?

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A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 6 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 5 of the 6 cups. (a) What are her chances of having her claim granted if she is in fact only guessing? (b) What are her chances of having her claim rejected when in fact she really does have the ability she claims?

Mathematics
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Are you allowed to use a graphing calculator for this? If you are, for part A you would use Binomial Cdf with 6 trials, a probability of .5, a lower value of 5, and an upper value of 6. The probability is only .5 because she would be guessing, and she only has two choices to guess from. As for part B, you would run Binomial Cdf again with 6 trials, a probability of .75, a lower value of 0, and an upper value of 4. The probability in this one is .75 because she does have that ability, but the values are below 5 in order to reject her claim. There's a way to do it by hand, but if I remember correctly, it's rather tedious.

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